• How to obtain RMS Value and Average Value

RMS Value and Average Value of Pulse Wave

The first illustration shows the root mean square (RMS) value and average value of a pulse wave (with a maximum value of \(V_M\) and a period of \(T\)).

Now, let’s explain how each of these values are calculated (we strive to include as many intermediate steps as possible).

Waveform of a Pulse Wave

To find the root mean square (RMS) value and average value of a pulse wave, we first need to express the pulse wave as a formula.

The pulse wave has different formulas for the red region \(\left(0 \leq t \lt T_1\right)\) and the blue region \(\left(T_1 \leq t \lt T\right)\).

Let’s calculate the formulas for the red region and blue region.

Red Region

The region “\(0 \leq t \lt T_1\)” corresponds to the red region.

The red line is always \(V_M\) during the time \(T_1\).

Therefore, the red region can be represented by the following formula.

\begin{eqnarray}
v(t)=V_M
\end{eqnarray}

Blue Region

The region “\(T_2 \leq t \lt T\)” corresponds to the blue region.

The blue rgsion is zero.

Therefore, the blue region can be represented by the following formula.

\begin{eqnarray}
v(t)=0
\end{eqnarray}

By combining the red region and the blue region, the pulse wave can be represented by the following formula.

\begin{eqnarray}
v(t) = \begin{cases}
V_M & \left(0 \leq t \lt T_1\right) \\
\\
0 & \left(T_1 \leq t \lt T\right)
\end{cases}
\end{eqnarray}

RMS Value of a Pulse Wave

The root mean square (RMS) value \(V_{RMS}\) of a waveform \(v(t)\) is the square root of the mean of the square of \(v(t)\). It can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{T} \displaystyle \int_{0}^{T}v(t)^2dt}
\end{eqnarray}

The red region is \(0 \leq t \lt T_1\)“, and the blue region is “\(T_1 \leq t \lt T\)“.

In the formula for finding the absolute value, if we separate the red region and the blue region, we get the following formula.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{T} \left(\displaystyle \int_{0}^{T_1}v(t)^2dt+\displaystyle \int_{T_1}^{T}v(t)^2dt\right )}\\
\\
&=& \sqrt{\displaystyle\frac{1}{T} \left(\displaystyle \int_{0}^{T_1}V_M^2dt+\displaystyle \int_{T_1}^{T}0\right )}\\
\\
&=& \sqrt{\displaystyle\frac{1}{T} \displaystyle \int_{0}^{T_1}V_M^2dt}
\end{eqnarray}

\(V_M^2\) is not a variable that changes with time \(t\), but a constant. Therefore, it can be taken out of the integration. As a result, the following equation is obtained.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{T_1} V_M^2\displaystyle \int_{0}^{T}1dt}\\
\\
&=& V_M\sqrt{\displaystyle\frac{1}{T_1} \displaystyle \int_{0}^{T}1dt}
\end{eqnarray}

When calculating the above equation, the following formula is obtained.

\begin{eqnarray}
V_{RMS} &=& V_M\sqrt{\displaystyle\frac{1}{T} \left[t\right]_{0}^{T_1}}\\
\\
&=& V_M\sqrt{\displaystyle\frac{1}{T} \left(T_1-0\right)}\\
\\
&=& \sqrt{\displaystyle\frac{T_1}{T}}V_M
\end{eqnarray}

Therefore, the root mean square (RMS) value \(V_{RMS}\) of the pulse wave is as follows.

\begin{eqnarray}
V_{RMS} =\sqrt{\displaystyle\frac{T_1}{T}}V_M
\end{eqnarray}

Average Value of a Pulse Wave

The average value \(V_{AVE}\) of a waveform \(v(t)\) is the average value of the absolute value \(|v(t)|\) of \(v(t)\) and can be represented by the following formula:

This formula for calculating the average value uses the absolute value \(|v(t)|\) of \(v(t)\).

Therefore, if there is a negative region in the waveform, it needs to be converted so that the negative region becomes positive.

In the case of a pulse wave, there is no negative region, so the formula for \(v(t)\) and the formula for the absolute value \(|v(t)|\) of \(v(t)\) become the same.

Therefore, the absolute value \(|v(t)|\) of \(v(t)\) can be represented by the following formula.

\begin{eqnarray}
|v(t)| = \begin{cases}
V_M & \left(0 \leq t \lt T_1\right) \\
\\
0 & \left(T_1 \leq t \lt T\right)
\end{cases}
\end{eqnarray}

In the formula to find the average value, if we separate each term, we get the following formula.

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{T} \displaystyle \int_{0}^{T}|v(t)|dt\\
\\
&=& \displaystyle\frac{1}{T} \left(\displaystyle \int_{0}^{T_1}|v(t)|dt+\displaystyle \int_{T_1}^{T}|v(t)|dt\right )\\
\end{eqnarray}

Since the pulse wave is zero in the region \(T_1 \leq t \lt T\), the above equation becomes:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{T} \left(\displaystyle \int_{0}^{T_1}|v(t)|dt+\displaystyle \int_{T_1}^{T}0dt\right )\\
\\
&=&\displaystyle\frac{1}{T} \displaystyle \int_{0}^{T_1}|v(t)|dt\\
\end{eqnarray}

In the above equation, when substituting \(v(t)=V_M\), the following formula is obtained.

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{T} \displaystyle \int_{0}^{T_1}V_Mdt\\
\\
&=& \displaystyle\frac{1}{T} V_M\displaystyle \int_{0}^{T_1}1dt\\
\\
&=& \displaystyle\frac{1}{T}V_M \left[t\right]_{0}^{T_1}\\
\\
&=& \displaystyle\frac{1}{T}V_M \left(T_1-0\right)\\
\\
&=&\displaystyle\frac{T_1}{T}V_M
\end{eqnarray}

Therefore, the average value \(V_{AVE}\) of the pulse wave is as follows.

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{T_1}{T}V_M
\end{eqnarray}

Summary

In this article, the following information on the “Pulse Wave“ was explained.

• How to obtain RMS Value and Average Value

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

• How to obtain RMS Value, Average Value, Form Factor, and Crest Factor

RMS Value, Average Value, Form Factor, and Crest Factor of Half-Wave Rectified Sine-Wave

The first illustration shows the root mean square (RMS) value, average value, form factor, and crest factor of a half-wave rectified sine-wave (with a maximum value of \(V_M\) and a period of \(T\)).

Now, let’s explain how each of these values are calculated (we strive to include as many intermediate steps as possible).

Waveform of a Half-Wave Rectified Sine-Wave

To find the root mean square (RMS) value and average value of a half-wave rectified sine-wave, we first need to express the half-wave rectified sine-wave as a formula.

The half-wave rectified sine-wave has different formulas for the red region \(\left(0 \leq t \lt \displaystyle \frac{T}{2}\right)\) and the blue region \(\left(\displaystyle \frac{T}{2} \leq t \lt T\right)\).

Let’s calculate the formulas for the red region and blue region.

Red Region

The region “\(0 \leq t \lt \displaystyle \frac{T}{2}\)” corresponds to the red region.

The red region is part of the waveform of \(V_M\sin{{\omega}t}\).

Therefore, the red region can be represented by the following formula.

\begin{eqnarray}
v(t)=V_M\sin{{\omega}t}
\end{eqnarray}

Blue Region

The region “\(\displaystyle \frac{T}{2} \leq t \lt T\)” corresponds to the blue region.

The blue region is zero.

Therefore, the blue region can be represented by the following formula.

\begin{eqnarray}
v(t)=0
\end{eqnarray}

By combining the red region and the blue region, the half-wave rectified sine-wave can be represented by the following formula.

\begin{eqnarray}
v(t) = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq t \lt \displaystyle \frac{T}{2}\right) \\
\\
0 & \left(\displaystyle \frac{T}{2} \leq t \lt T\right)
\end{cases}
\end{eqnarray}

Next, we will calculate the RMS value, average value, form factor, and crest factor of the half-wave rectified sine-wave. However, using the above formula can make the calculation slightly complex.

Therefore, to simplify the calculation this time, we will convert the time axis (horizontal axis \(t\)) to the phase axis (horizontal axis \({{\omega}t}\)).

When the time axis (horizontal axis \(t\)) is converted to the phase axis (horizontal axis \({{\omega}t}\)), the half-wave rectified sine-wave becomes the following formula.

\begin{eqnarray}
v({\omega}t) = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq {\omega}t \lt \pi\right) \\
\\
0 & \left(\pi \leq {\omega}t \lt 2\pi\right)
\end{cases}
\end{eqnarray}

RMS Value of a Half-Wave Rectified Sine-Wave

The root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) is the square root of the mean of the square of \(v({{\omega}t})\). It can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}v({{\omega}t})^2d({{\omega}t}})
\end{eqnarray}

The red region is \(0 \leq {\omega}t \lt \pi\)“, and the blue region is “\(\pi \leq {\omega}t \lt 2\pi\)“.

In the formula for finding the absolute value, if we separate the red region and the blue region, we get the following formula.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \left(\displaystyle \int_{0}^{\pi}v({{\omega}t})^2d({\omega}t)+\displaystyle \int_{\pi}^{2\pi}v({{\omega}t})^2d({\omega}t)\right )}\\
\\
&=& \sqrt{\displaystyle\frac{1}{2\pi} \left(\displaystyle \int_{0}^{\pi}(V_M\sin{{\omega}t})^2d({\omega}t)+\displaystyle \int_{\pi}^{2\pi}0^2d({\omega}t)\right )}\\
\\
&=& \sqrt{\displaystyle\frac{1}{2\pi}\displaystyle \int_{0}^{\pi}(V_M\sin{{\omega}t})^2d({\omega}t)}
\end{eqnarray}

The formula for the red region is \(V_M\sin{{\omega}t}\), and the formula for the blue region is \(-V_M\sin{{\omega}t}\), but in the calculation of the effective value, we square it, so we can combine the above formulas. If we combine them, we get the following formula.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{\pi} \displaystyle \int_{0}^{2\pi}(V_M\sin{{\omega}t})^2d({\omega}t)}
\end{eqnarray}

In the above formula, if you let

\begin{eqnarray}
X &=& \displaystyle \int_{0}^{\pi}(V_M\sin{{\omega}t})^2 d({\omega}t)
\end{eqnarray}

then the root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} X}
\end{eqnarray}

Next, we calculate the value of \(X\).

\begin{eqnarray}
X &=& \displaystyle \int_{0}^{\pi}v({{\omega}t})^2 d({\omega}t)\\
\\
&=& \displaystyle \int_{0}^{\pi}{V_M}^2{\sin}^2{\omega}t d({\omega}t)\\
\\
&=& {V_M}^2\displaystyle \int_{0}^{\pi}{\sin}^2{\omega}t d({\omega}t)\\
\\
&=& {V_M}^2\displaystyle \int_{0}^{\pi}\displaystyle \frac{1-{\cos2{\omega}t}}{2} d({\omega}t)\\
\\
&=& {V_M}^2 \left[\displaystyle\frac{1}{2}{{\omega}t}-\frac{1}{4}{\sin2{\omega}t} \right]_{0}^{\pi}\\
\\
&=& {V_M}^2 \left( \displaystyle\frac{1}{2}×{\pi}-\frac{1}{4}{\sin{2\pi}}\right)\\
\\
&=& \displaystyle\frac{{V_M}^2 {\pi}}{2}
\end{eqnarray}

Therefore, the root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) becomes:

\begin{eqnarray}
V_{RMS} &=&\sqrt{\displaystyle\frac{1}{2\pi} X}\\
\\
&=&\sqrt{\displaystyle\frac{1}{2\pi} \displaystyle\frac{{V_M}^2 {\pi}}{2}}\\
\\
&=&\displaystyle\frac{1}{2}V_M
\end{eqnarray}

Average Value of a Half-Wave Rectified Sine-Wave

The average value \(V_{AVE}\) of a waveform \(v({{\omega}t})\) is the average value of the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) and can be represented by the following formula:

This formula for calculating the average value uses the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\).

Therefore, if there is a negative region in the waveform, it needs to be converted so that the negative region becomes positive.

In the case of a half-wave rectified sine-wave, there is no negative region, so the formula for \(v({{\omega}t})\) and the formula for the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) become the same.

Therefore, the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) can be represented by the following formula.

\begin{eqnarray}
|v({{\omega}t})| = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq {\omega}t \lt \pi\right) \\
\\
0 & \left(\pi \leq {\omega}t \lt 2\pi\right)
\end{cases}
\end{eqnarray}

In the formula to find the average value, if we separate each term, we get the following formula.

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}|v({\omega}t)|d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{2\pi}\left(\displaystyle \int_{0}^{\pi}|v({\omega}t)|d({{\omega}t})+ \int_{\pi}^{2\pi}|v({\omega}t)|d({{\omega}t}) \right)\\
\end{eqnarray}

Since the half-wave rectified sine-wave is zero in the region \(\pi \leq {\omega}t \lt 2\pi\), the above equation becomes:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi}\displaystyle \int_{0}^{\pi}|v({\omega}t)|d({{\omega}t})
\end{eqnarray}

If we calculate the above formula, the average value \(V_{AVE}\) of the half-wave rectified sine-wave becomes:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi}\displaystyle \int_{0}^{\pi}V_M\sin{{\omega}t}d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{2\pi}V_M\left[-\cos{\omega}t \right]_{0}^{\pi}\\
\\
&=& \displaystyle\frac{V_M}{2\pi}\left(-\cos\pi + \cos0 \right)\\
\\
&=& \displaystyle\frac{1}{\pi}V_M
\end{eqnarray}

Form Factor of a Half-Wave Rectified Sine-Wave

The form factor can be represented by the following formula:

\begin{eqnarray}
\mbox{Form Factor} &=& \displaystyle\frac{\mbox{Root Mean Square Value}~~V_{RMS}}{\mbox{Average Value}~~V_{AVE}}
\end{eqnarray}

Since we’ve already calculated the root mean square (RMS) value \(V_{RMS}\) and average value \(V_{AVE}\) of the sine wave, we can substitute these values into the formula to calculate the form factor of the half-wave rectified sine-wave.

\begin{eqnarray}
\mbox{Form Factor} = \displaystyle\frac{\displaystyle\frac{1}{2}V_M}{\displaystyle\frac{1}{\pi}V_M} = \displaystyle\frac{\pi}{2}
\end{eqnarray}

Maximum Value of a Half-Wave Rectified Sine-Wave

As can be seen from the waveform, the maximum value \(V_{PEAK}\)​ of a half-wave rectified sine-wave is represented by the following value:

\begin{eqnarray}
\mbox{Maximum Value}~~V_{PEAK}=V_M
\end{eqnarray}

Crest Factor of a Half-Wave Rectified Sine-Wave

The Crest factor can be represented by the following formula:

\begin{eqnarray}
\mbox{Crest Factor} &=& \displaystyle\frac{\mbox{Peak Value}~~V_{PEAK}}{\mbox{Root Mean Square Value}~~V_{RMS}}
\end{eqnarray}

Since we’ve already calculated the root mean square (RMS) value \(V_{RMS}\) and peak value \(V_{PEAK}\) of the sine wave, we can substitute these values into the formula to calculate the peak factor (crest factor) of the half-wave rectified sine-wave.

The Crest factor of the half-wave rectified sine-wave is represented by the following value:

\begin{eqnarray}
\mbox{Crest Factor} = \displaystyle\frac{V_M}{\displaystyle\frac{1}{2}V_M} = 2
\end{eqnarray}

Summary

In this article, the following information on the “Half-Wave Rectified Sine-Wave“ was explained.

• How to obtain RMS Value, Average Value, Form Factor, and Crest Factor

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

• How to obtain RMS Value, Average Value, Form Factor, and Crest Factor

RMS Value, Average Value, Form Factor, and Crest Factor of Full-Wave Rectified Sine-Wave

The first illustration shows the root mean square (RMS) value, average value, form factor, and crest factor of a full-wave rectified sine-wave (with a maximum value of \(V_M\) and a period of \(T\)).

Now, let’s explain how each of these values are calculated (we strive to include as many intermediate steps as possible).

Waveform of a Full-Wave Rectified Sine-Wave

To find the root mean square (RMS) value and average value of a full-wave rectified sine-wave, we first need to express the full-wave rectified sine-wave as a formula.

The full-wave rectified sine-wave has different formulas for the red region \(\left(0 \leq t \lt \displaystyle \frac{T}{2}\right)\) and the blue region \(\left(\displaystyle \frac{T}{2} \leq t \lt T\right)\).

Let’s calculate the formulas for the red region and blue region.

Red Region

The region “\(0 \leq t \lt \displaystyle \frac{T}{2}\)” corresponds to the red region.

The red region is part of the waveform of \(V_M\sin{{\omega}t}\).

Therefore, the red region can be represented by the following formula.

\begin{eqnarray}
v(t)=V_M\sin{{\omega}t}
\end{eqnarray}

Blue Region

The region “\(\displaystyle \frac{T}{2} \leq t \lt T\)” corresponds to the blue region.

The blue region is an inverted waveform of \(V_M\sin{{\omega}t}\).

Therefore, the blue region can be represented by the following formula.

\begin{eqnarray}
v(t)=-V_M\sin{{\omega}t}
\end{eqnarray}

By combining the red region and the blue region, the full-wave rectified sine-wave can be represented by the following formula.

\begin{eqnarray}
v(t) = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq t \lt \displaystyle \frac{T}{2}\right) \\
\\
-V_M\sin{{\omega}t} & \left(\displaystyle \frac{T}{2} \leq t \lt T\right)
\end{cases}
\end{eqnarray}

Next, we will calculate the RMS value, average value, form factor, and crest factor of the full-wave rectified sine-wave. However, using the above formula can make the calculation slightly complex.

Therefore, to simplify the calculation this time, we will convert the time axis (horizontal axis \(t\)) to the phase axis (horizontal axis \({{\omega}t}\)).

When the time axis (horizontal axis \(t\)) is converted to the phase axis (horizontal axis \({{\omega}t}\)), the full-wave rectified sine-wave becomes the following formula.

\begin{eqnarray}
v({\omega}t) = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq {\omega}t \lt \pi\right) \\
\\
-V_M\sin{{\omega}t} & \left(\pi \leq {\omega}t \lt 2\pi\right)
\end{cases}
\end{eqnarray}

RMS Value of a Full-Wave Rectified Sine-Wave

The root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) is the square root of the mean of the square of \(v({{\omega}t})\). It can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}v({{\omega}t})^2d({{\omega}t}})
\end{eqnarray}

The red region is \(0 \leq {\omega}t \lt \pi\)“, and the blue region is “\(\pi \leq {\omega}t \lt 2\pi\)“.

In the formula for finding the absolute value, if we separate the red region and the blue region, we get the following formula.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \left(\displaystyle \int_{0}^{\pi}v({{\omega}t})^2d({\omega}t)+\displaystyle \int_{\pi}^{2\pi}v({{\omega}t})^2d({\omega}t)\right )}\\
\\
&=& \sqrt{\displaystyle\frac{1}{2\pi} \left(\displaystyle \int_{0}^{\pi}(V_M\sin{{\omega}t})^2d({\omega}t)+\displaystyle \int_{\pi}^{2\pi}(-V_M\sin{{\omega}t})^2d({\omega}t)\right )}
\end{eqnarray}

The formula for the red region is \(V_M\sin{{\omega}t}\), and the formula for the blue region is \(-V_M\sin{{\omega}t}\), but in the calculation of the effective value, we square it, so we can combine the above formulas. If we combine them, we get the following formula.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}(V_M\sin{{\omega}t})^2d({\omega}t)}
\end{eqnarray}

In the above formula, if you let

\begin{eqnarray}
X &=& \displaystyle \int_{0}^{2\pi}(V_M\sin{{\omega}t})^2 d({\omega}t)
\end{eqnarray}

then the root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} X}
\end{eqnarray}

Next, we calculate the value of \(X\).

\begin{eqnarray}
X &=& \displaystyle \int_{0}^{2\pi}(V_M\sin{{\omega}t})^2 d({\omega}t)\\
\\
&=& \displaystyle \int_{0}^{2\pi}{V_M}^2{\sin}^2{\omega}t d({\omega}t)\\
\\
&=& {V_M}^2\displaystyle \int_{0}^{2\pi}{\sin}^2{\omega}t d({\omega}t)\\
\\
&=& {V_M}^2\displaystyle \int_{0}^{2\pi}\displaystyle \frac{1-{\cos2{\omega}t}}{2} d({\omega}t)\\
\\
&=& {V_M}^2 \left[\displaystyle\frac{1}{2}{{\omega}t}-\frac{1}{4}{\sin2{\omega}t} \right]_{0}^{2\pi}\\
\\
&=& {V_M}^2 \left( \displaystyle\frac{1}{2}×{2\pi}-\frac{1}{4}{\sin{4\pi}}\right)\\
\\
&=& {V_M}^2 {\pi}
\end{eqnarray}

Therefore, the root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) becomes:

\begin{eqnarray}
V_{RMS} &=&\sqrt{\displaystyle\frac{1}{2\pi} X}\\
\\
&=&\sqrt{\displaystyle\frac{1}{2\pi} {V_M}^2 {\pi}}\\
\\
&=&\displaystyle\frac{1}{\sqrt{2}}V_M
\end{eqnarray}

Average Value of a Full-Wave Rectified Sine-Wave

The average value \(V_{AVE}\) of a waveform \(v({{\omega}t})\) is the average value of the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) and can be represented by the following formula:

This formula for calculating the average value uses the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\).

Therefore, if there is a negative region in the waveform, it needs to be converted so that the negative region becomes positive.

In the case of a full-wave rectified sine-wave, there is no negative region, so the formula for \(v({{\omega}t})\) and the formula for the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) become the same.

Therefore, the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) can be represented by the following formula.

\begin{eqnarray}
|v({{\omega}t})| = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq {\omega}t \lt \pi\right) \\
\\
-V_M\sin{{\omega}t} & \left(\pi \leq {\omega}t \lt 2\pi\right)
\end{cases}
\end{eqnarray}

In the formula to find the average value, if we separate each term, we get the following formula.

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}|v({\omega}t)|d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{2\pi}\left(\displaystyle \int_{0}^{\pi}|v({\omega}t)|d({{\omega}t})+ \int_{\pi}^{2\pi}|v({\omega}t)|d({{\omega}t}) \right)\\
\end{eqnarray}

This formula integrates the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) over the region from \(0\) to \(2\pi\), and finally divides by \(2\pi\) to find the average value.

However, as shown in the diagram below, integrating over the region from \(0\) to \(\pi\) and finally dividing by π yields the same average value.

Therefore, the average value of the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) can be calculated by the following formula:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{\pi} \displaystyle \int_{0}^{\pi}|v({\omega}t)|d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{\pi}\displaystyle \int_{0}^{\pi}V_M\sin{{\omega}t}d({{\omega}t})
\end{eqnarray}

If we calculate the above formula, the average value \(V_{AVE}\) of the full-wave rectified sine-wave becomes:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{\pi}\displaystyle \int_{0}^{\pi}V_M\sin{{\omega}t}d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{\pi}V_M\left[-\cos{\omega}t \right]_{0}^{\pi}\\
\\
&=& \displaystyle\frac{V_M}{\pi}\left(-\cos\pi – \cos0 \right)\\
\\
&=& \displaystyle\frac{2V_M}{\pi}
\end{eqnarray}

Form Factor of a Full-Wave Rectified Sine-Wave

The form factor can be represented by the following formula:

\begin{eqnarray}
\mbox{Form Factor} &=& \displaystyle\frac{\mbox{Root Mean Square Value}~~V_{RMS}}{\mbox{Average Value}~~V_{AVE}}
\end{eqnarray}

Since we’ve already calculated the root mean square (RMS) value \(V_{RMS}\) and average value \(V_{AVE}\) of the sine wave, we can substitute these values into the formula to calculate the form factor of the full-wave rectified sine-wave.

\begin{eqnarray}
\mbox{Form Factor} = \displaystyle\frac{\displaystyle\frac{1}{\sqrt{2}}V_M}{\displaystyle\frac{2V_M}{\pi}} = \displaystyle\frac{\pi}{2\sqrt{2}}
\end{eqnarray}

Maximum Value of a Full-Wave Rectified Sine-Wave

As can be seen from the waveform, the maximum value \(V_{PEAK}\)​ of a full-wave rectified sine-wave is represented by the following value:

\begin{eqnarray}
\mbox{Maximum Value}~~V_{PEAK}=V_M
\end{eqnarray}

Crest Factor of a Full-Wave Rectified Sine-Wave

The Crest factor can be represented by the following formula:

\begin{eqnarray}
\mbox{Crest Factor} &=& \displaystyle\frac{\mbox{Peak Value}~~V_{PEAK}}{\mbox{Root Mean Square Value}~~V_{RMS}}
\end{eqnarray}

Since we’ve already calculated the root mean square (RMS) value \(V_{RMS}\) and peak value \(V_{PEAK}\) of the sine wave, we can substitute these values into the formula to calculate the peak factor (crest factor) of the full-wave rectified sine-wave.

The Crest factor of the full-wave rectified sine-wave is represented by the following value:

\begin{eqnarray}
\mbox{Crest Factor} = \displaystyle\frac{V_M}{\displaystyle\frac{1}{\sqrt{2}}V_M} = \sqrt{2}
\end{eqnarray}

Summary

In this article, the following information on the “Full-Wave Rectified Sine-Wave“ was explained.

• How to obtain RMS Value, Average Value, Form Factor, and Crest Factor

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

Difference between “Average Value” and “RMS Value”

First, let’s briefly explain the difference between “Average Value” and “RMS Value” (we will explain each in detail later).

Taking the sine wave \(v=V_M\sin{{\omega}t}\) as an example:

Please refer to the following article for the derivation of the above formula. It explains in detail why the average value \(V_{AVE}\) of the sine wave becomes \(\displaystyle\frac{2V_M}{\pi}\), and why the RMS value \(V_{RMS}\) of the sine wave becomes \(\displaystyle\frac{V_M}{\sqrt{2}}\).

Average Value

Let’s consider the sine wave \(v=V_M\sin{{\omega}t}\) as an example.

Since the average of the ‘positive’ and ‘negative’ of AC becomes ‘0’, the average value \(V_{AVE}\) is the average of the absolute value \(|v|\) of the sine wave \(v\). Therefore, the formula to calculate the average value \(V_{AVE}\) is represented by the following formula.

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}|v|d({{\omega}t})\\
\\
&=&\displaystyle\frac{2V_M}{\pi}
\end{eqnarray}

As shown in the following figure, the above formula simply indicates that the areas are equal.

Supplement

The average value \(V_{AVE}\) is used when calculating losses (power consumption) for things where voltage remains constant regardless of the current (such as the forward voltage of a diode).

For example, if the average value of the current flowing through a diode with a forward voltage \(V_{F}\) is \(I_{AVE}\), the loss (power consumption) \(P_{D}\) at the diode is represented by the following formula.

\begin{eqnarray}
P_{D} &=& V_{F} I_{AVE}
\end{eqnarray}

RMS Value

Let’s consider the sine wave \(v=V_M\sin{{\omega}t}\) as an example.

The RMS value \(V_{RMS}\) is what you get when you take the square root (\(\sqrt{}\)) of the average value of the squared sine wave \(v^2\).

Therefore, the formula to calculate the RMS value \(V_{RMS}\) is represented by the following formula.

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}v^2d({{\omega}t}})\
\end{eqnarray}

But why does it turn out to be this formula?

This is because the RMS value is the “value of the voltage that generates the same power when a DC voltage is applied to the resistance” (it’s a bit complicated…).

To explain it in an easy-to-understand way, let’s take a square wave v as an example, with a peak value \(V_M\) of \(1{\mathrm{[V]}}\) and a duty ratio \(D\) of \(0.5\).

RMS Value \(V_{RMS}\) of Square Wave \(v\)

First, let’s calculate the RMS value \(V_{RMS}\) of the square wave \(v\).

When you square the square wave \(v\), the first half of the period becomes \(0{\mathrm{[V]}}\) and the second half of the period becomes \(1{\mathrm{[V]}}\).

Therefore, the average value of the squared square wave \(v^2\) is \(\displaystyle\frac {1}{2}{\mathrm{[V]}}\).

Take the square root (\(\sqrt{}\)) of this average value results in \(\displaystyle\frac {1}{\sqrt{2}}{\mathrm{[V]}}\).

In other words, the RMS value \(V_{RMS}\) of the square wave \(v\), with a peak value \(V_M\) of \(1{\mathrm{[V]}}\) and a duty ratio \(D\) of \(0.5\), is \(\displaystyle\frac {1}{\sqrt{2}}{\mathrm{[V]}}\).

Power When Square Wave \(v\) is applied to Resistance \(R\)

Next, let’s calculate the power when the square wave \(v\) is applied to the resistance.

Consider the power \(P_R\) when a square wave \(v\), with a peak value \(V_M\) of \(1{\mathrm{[V]}}\) and a duty ratio \(D\) of \(0.5\), is applied to a resistance \(R\) of \(1Ω\).

The power consumed during the first half of \(0{\mathrm{[V]}}\) period is as follows:

\begin{eqnarray}
P_R=\frac{V^2}{R}=\frac{0^2}{1}=0{\mathrm{[W]}}
\end{eqnarray}

The power consumed during the second half of \(1{\mathrm{[V]}}\) period is as follows:

\begin{eqnarray}
P_R=\frac{V^2}{R}=\frac{1^2}{1}=1{\mathrm{[W]}}
\end{eqnarray}

Therefore, the average power \(P_{AVE}\) is given by the following formula:

\begin{eqnarray}
P_{AVE}=\displaystyle\frac {1}{2}{\mathrm{[W]}}
\end{eqnarray}

Power When DC Voltage \(V\) is Applied to Resistance \(R\)

Here, consider the case when the power becomes \(\displaystyle\frac {1}{2}{\mathrm{[W]}}\) when a DC voltage \(V\) is applied to a resistance \(R\) of \(1Ω\). The following equation holds:

\begin{eqnarray}
\displaystyle\frac {1}{2}{\mathrm{[W]}}&=&\frac{V^2}{1}\\
\\
{\Leftrightarrow}V&=&\displaystyle\frac {1}{\sqrt{2}}{\mathrm{[V]}}
\end{eqnarray}

You can see that this matches the RMS value \(V_{RMS}\) that we calculated earlier.

From the above, it can be understood that the RMS value \(V_{RMS}\) is the value of the voltage that generates the same power as when a DC voltage \(V\) is applied to the resistance.

Using RMS Value When Calculating Resistance Load Loss

The RMS value is used when voltage and current are proportional, i.e., when calculating the loss (power consumption) of a resistive load.

For example, if the average value of the voltage applied to a resistance \(R\) is \(V_{RMS}\) and the RMS value of the current flowing at that time is \(I_{RMS}\), the loss (power consumption) \(P_{R}\) at the resistance is given by the following formula:

\begin{eqnarray}
P_{R}=\displaystyle\frac {{V_{RMS}}^2}{R}=R{I_{RMS}}^2
\end{eqnarray}

Summary

In this article, the following information on the “Average Value” and “RMS Value” was explained.

• The difference between “Average Value” and “RMS Value”

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

• How to obtain RMS Value, Average Value, Form Factor, and Crest Factor

RMS Value, Average Value, Form Factor, and Crest Factor of Sine Wave

The first illustration shows the root mean square (RMS) value, average value, form factor, and crest factor of a sine wave (with a maximum value of \(V_M\) and a period of \(T\)).

Now, let’s explain how each of these values are calculated (we strive to include as many intermediate steps as possible).

Waveform of a Sine Wave

To find the root mean square (RMS) value and average value of a sine wave, we first need to express the sine wave as a formula.

Here is the waveform of a sine wave:

In the above figure, the sine wave can be represented by the following formula:

\begin{eqnarray}
v(t)=V_M\sin{{\omega}t}
\end{eqnarray}

Using the above formula, we can calculate the root mean square (RMS) value, average value, form factor, and peak factor of the sine wave.

However, calculations become a bit complex with this formula.

Therefore, for easier computation, we will convert the time axis (horizontal axis \(t\))) to the phase axis (change the horizontal axis to \({{\omega}t}\)).

About the benefits and method of converting the time axis (horizontal axis t) to the phase axis (horizontal axis ωt)

Benefits of Conversion

For instance, if you integrate \(\sin{{\omega}t}\) with respect to time \(t\), you get the following equation:

\begin{eqnarray}
\displaystyle \int \sin{{\omega}t} dt = -\displaystyle \frac{1}{\omega}\cos{{\omega}t} +C\\
C：\mbox{constant of integration}
\end{eqnarray}

Integrating with respect to time \(t\) introduces \({\omega}\) in the denominator, making the calculation complex.

On the other hand, if you integrate \(\sin{{\omega}t}\) with respect to phase \({{\omega}t}\), you get:

\begin{eqnarray}
\displaystyle \int \sin{{\omega}t} d({{\omega}t}) = -\cos{{\omega}t} +C\\
C：\mbox{constant of integration}
\end{eqnarray}

As you can see from the above equation, integrating with respect to phase \({{\omega}t}\) does not introduce \({\omega}\) in the denominator. Therefore, it simplifies the calculation.

Method of Conversion

Let’s explain the method of conversion.

Since time is “\(t\)” and phase is “\({{\omega}t}\)”, to convert time \(t\) into phase \({{\omega}t}\), you multiply time \(t\) by \({\omega}\).

If you represent the period at time \(t\) as \(T\), the period at phase \({{\omega}t}\) is obtained by multiplying the period \(T\) by \({\omega}\).

The calculation is as follows:

\begin{eqnarray}
\mbox{Period at phase}~~{{\omega}t}={\omega}T=2{\pi}f×T=2{\pi}\displaystyle \frac{1}{T}×T=2{\pi}
\end{eqnarray}

From here, we will use the phase axis (horizontal axis \({{\omega}t}\)) in the figure below to calculate the root mean square, average value, form factor, and peak factor of the sine wave.

RMS Value of a Sine Wave

The root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) is the square root of the mean of the square of \(v({{\omega}t})\). It can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}v({{\omega}t})^2d({{\omega}t}})
\end{eqnarray}

In the above formula, if you let

\begin{eqnarray}
X &=& \displaystyle \int_{0}^{2\pi}v({{\omega}t})^2 d({\omega}t)
\end{eqnarray}

then the root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) can be represented by the following formula:

\begin{eqnarray}
V_{RMS} &=& \sqrt{\displaystyle\frac{1}{2\pi} X}
\end{eqnarray}

Next, we calculate the value of \(X\).

\begin{eqnarray}
X &=& \displaystyle \int_{0}^{2\pi}v({{\omega}t})^2 d({\omega}t)\\
\\
&=& \displaystyle \int_{0}^{2\pi}{V_M}^2{\sin}^2{\omega}t d({\omega}t)\\
\\
&=& {V_M}^2\displaystyle \int_{0}^{2\pi}{\sin}^2{\omega}t d({\omega}t)\\
\\
&=& {V_M}^2\displaystyle \int_{0}^{2\pi}\displaystyle \frac{1-{\cos2{\omega}t}}{2} d({\omega}t)\\
\\
&=& {V_M}^2 \left[\frac{1}{2}{{\omega}t}-\frac{1}{4}{\sin2{\omega}t} \right]_{0}^{2\pi}\\
\\
&=& {V_M}^2 \left( \frac{1}{2}×{2\pi}-\frac{1}{4}{\sin{4\pi}}\right)\\
\\
&=& {V_M}^2 {\pi}
\end{eqnarray}

Therefore, the root mean square (RMS) value \(V_{RMS}\) of a waveform \(v({{\omega}t})\) becomes:

\begin{eqnarray}
V_{RMS} &=&\sqrt{\displaystyle\frac{1}{2\pi} X}\\
\\
&=&\sqrt{\displaystyle\frac{1}{2\pi} {V_M}^2 {\pi}}\\
\\
&=&\displaystyle\frac{V_M}{\sqrt{2}}
\end{eqnarray}

Average Value of a Sine Wave

The average value \(V_{AVE}\) of a waveform \(v({{\omega}t})\) is the average value of the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) and can be represented by the following formula:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}|v({{\omega}t})|d({{\omega}t})
\end{eqnarray}

This formula for calculating the average value uses the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\).

Therefore, you need to convert the negative region of the waveform (the lightly shaded blue area) to positive (the lightly shaded red area).

For the region \(\left(0 \leq {\omega}t \lt \pi \right)\), where the waveform \(v({{\omega}t})\) is positive, no conversion is necessary.

For the region \(\left(\pi \leq {\omega}t \lt 2\pi \right)\), where the waveform \(v({{\omega}t})\) is negative, you must multiply by -1 to make it positive.

Therefore, the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) can be represented by the following formula:

\begin{eqnarray}
|v({{\omega}t})| = \begin{cases}
V_M\sin{{\omega}t} & \left(0 \leq {\omega}t \lt \pi\right) \\
\\
-V_M\sin{{\omega}t} & \left(\pi \leq {\omega}t \lt 2\pi\right)
\end{cases}
\end{eqnarray}

In the formula to calculate the average value, if we separate each part, we get:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{2\pi} \displaystyle \int_{0}^{2\pi}|v({\omega}t)|d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{2\pi}\left(\displaystyle \int_{0}^{\pi}V_M\sin{{\omega}t}d({{\omega}t})+ \int_{\pi}^{2\pi}-V_M\sin{{\omega}t}d({{\omega}t}) \right)\\
\end{eqnarray}

This formula integrates the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) over the region from \(0\) to \(2\pi\) and then divides by \(2\pi\) to find the average value.

However, if we consider the diagram, integrating over the region from \(0\) to \(\pi\) and then dividing by \(\pi\) yields the same average value.

Conceptually, it is as shown in the figure below:

Therefore, the average value of the absolute value \(|v({{\omega}t})|\) of \(v({{\omega}t})\) can be calculated by the following formula:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{\pi} \displaystyle \int_{0}^{\pi}|v({\omega}t)|d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{\pi}\displaystyle \int_{0}^{\pi}V_M\sin{{\omega}t}d({{\omega}t})
\end{eqnarray}

If we calculate the above formula, the average value \(V_{AVE}\) of the sine wave becomes:

\begin{eqnarray}
V_{AVE} &=& \displaystyle\frac{1}{\pi}\displaystyle \int_{0}^{\pi}V_M\sin{{\omega}t}d({{\omega}t})\\
\\
&=& \displaystyle\frac{1}{\pi}V_M\left[-\cos{\omega}t \right]_{0}^{\pi}\\
\\
&=& \displaystyle\frac{V_M}{\pi}\left(-\cos\pi – \cos0 \right)\\
\\
&=& \displaystyle\frac{2V_M}{\pi}
\end{eqnarray}

Form Factor of a Sine Wave

The form factor can be represented by the following formula:

\begin{eqnarray}
\mbox{Form Factor} &=& \displaystyle\frac{\mbox{Root Mean Square Value}~~V_{RMS}}{\mbox{Average Value}~~V_{AVE}}
\end{eqnarray}

Since we’ve already calculated the root mean square (RMS) value \(V_{RMS}\) and average value \(V_{AVE}\) of the sine wave, we can substitute these values into the formula to calculate the form factor of the sine wave.

\begin{eqnarray}
\mbox{Form Factor} = \displaystyle\frac{\displaystyle\frac{V_M}{\sqrt{2}}}{\displaystyle\frac{2V_M}{\pi}} = \displaystyle\frac{\pi}{2\sqrt{2}}
\end{eqnarray}

Maximum Value of a Sine Wave

As can be seen from the waveform, the maximum value \(V_{PEAK}\)​ of a sine wave is represented by the following value:

\begin{eqnarray}
\mbox{Maximum Value}~~V_{PEAK}=V_M
\end{eqnarray}

Crest Factor of a Sine Wave

The Crest factor can be represented by the following formula:

\begin{eqnarray}
\mbox{Crest Factor} &=& \displaystyle\frac{\mbox{Peak Value}~~V_{PEAK}}{\mbox{Root Mean Square Value}~~V_{RMS}}
\end{eqnarray}

Since we’ve already calculated the root mean square (RMS) value \(V_{RMS}\) and peak value \(V_{PEAK}\) of the sine wave, we can substitute these values into the formula to calculate the peak factor (crest factor) of the sine wave.

The Crest factor of the sine wave is represented by the following value:

\begin{eqnarray}
\mbox{Crest Factor} = \displaystyle\frac{V_M}{\displaystyle\frac{V_M}{\sqrt{2}}} = \sqrt{2}
\end{eqnarray}

Summary

In this article, the following information on the “Sine Wave“ was explained.

• How to obtain RMS Value, Average Value, Form Factor, and Crest Factor

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

For example, SOP, QFN and BGA are some of the package names, but it is very difficult to understand which package represents which shape.

Therefore, in this article, we have summarized the types and characteristics of each package in an easy-to-understand manner using diagrams. We hope you will find it helpful.

List of IC Package Types

The figure above shows the classification of packages. Packages can be broadly classified according to the following aspects.

• Difference in mounting method
  • Whether the mounting method is “insertion mounting” or “surface mounting“.
• Difference in terminals
  • Whether the terminals (leads, etc.) are “from 1 side“, “from 2 sides“, “from 4 sides“, or “in a grid“.

Now, we will explain each package in detail.

Types of IC Packages for Insertion Mounting

There are SIP, DIP, ZIP, and LGA packages for insertion mounting.

The main points of SIP, DIP, and ZIP are shown below (LGA will be explained in detail later).

We will now describe each package in turn.

Single In-line Package (SIP)

SIP stands for “Single In-line Package”.

Single In-line Package (SIP) is a package in which the leads come out of one side of the package, the leads are in a single row, and the package is for insert mounting. SIP is sometimes described as SIL.

Single In-line Package (SIP) has 2 to 23 pins.

The number after SIP indicates the number of pins. For example, SIP10 means a 10-pin SIP.

Single In-line Package (SIP) has the leads on the long side of the package and is mounted upright on the PCB. Since the package can be mounted upright, the mounting density of the PCB can be increased compared to the Dual In-line Package (DIP).

SIP is used not only in IC but also in network resistors and transistor arrays that require heat dissipation.

There are various types of SIP, such as HSIP and P-SIP.

Zig-zag In-line Package (ZIP)

ZIP stands for “Zig-zag In-line Package”.

Zig-zag In-line Package (ZIP) is a package in which the leads come out of one side of the package, the leads alternately zig-zagged out, and the package is for insert mounting.

Zig-zag In-line Package (ZIP) has 12 to 40 pins.

The number after ZIP indicates the number of pins. For example, ZIP12 means a 12-pin ZIP.

It is the same as Single In-line Package (SIP) in that the leads come out of one side of the package. However, the Zig-zag In-line Package (ZIP) has a zigzag shape of the lead, which allows the pin pitch to be shortened, thus shortening the long side.

The pin pitch of the ZIP (Zig-zag In-line Package) is 50 mils when the package face is viewed from the front, but 100 mils when it is inserted into the PCB.

There are various types of ZIP, such as SZIP and HZIP.

Dual In-line Package (DIP)

DIP stands for “Dual In-line Package”.

Dual In-line Package (DIP) is a package in which the leads come out of two sides of the package, the leads extend downward from the two long sides of the package, and the package is for insert mounting.

Dual In-line Package (DIP) has 6 to 64 pins.

The number after DIP indicates the number of pins. For example, DIP16 means a 16-pin DIP.

Dual In-line Package (DIP) is available in a variety of pin pitch distances. The normal pin pitch is 100 mils (2.54mm), but there are some with a pin pitch of 70 mils (1.778mm). Package widths include 600 mils (15.2mm), 400 mils (10.16mm), and 300 mils (7.62mm).

There are various types of DIP, such as SDIP and HSDIP.

Types of IC Packages for Surface Mounting

The following types of packages are available for insertion mounting.

Packages with leads coming out of two sides of the package are often marked with SO. SO stands for “Small Outline“. The shape of the lead is determined by the letter that comes after the SO, as shown below.

Packages with leads coming out of four sides of the package are often marked with QF. QF stands for “Quad Flat“. The shape of the lead is determined by the letter that comes after the QF, as shown below.

Packages with terminals arranged in a grid pattern from the bottom of the package are often marked with GA. GA stands for “Grid Array“. The shape of the lead is determined by the letter that comes before the GA, as shown below.

Now, we will explain each package in detail.

Small Outline Package (SOP)

SOP stands for “Small Outline Package”.

Small Outline Package (SOP) is a gull wing (L-shaped) package with leads coming out of two sides of the package. The pin pitch of the SOP (Small Outline Package) is 50 mils (1.27mm).

The number after SOP indicates the number of pins. For example, SOP8 means a 8-pin SOP.

In packages with a pin pitch of 1.27mm, those with a JEITA standard are SOP (Small Outline Package) and those with a JEDEC standard are SOIC (Small Outline Integrated Circuit). Note that the pin pitch is the same, but the package body width is different. SOIC is also sometimes referred to as “SOL (Small Outline L-leaded package)” or “SO”.

In addition, those with gull wing (L-shaped) leads coming out of the four sides of the package are called Quad Flat Package (QFP).

There are various types of SOP, such as SSOP and MSOP.

Small Outline J-leaded package (SOJ)

SOJ stands for “Small Outline J-leaded package”.

Small Outline J-leaded package (SOJ) is a J-leaded package with leads coming out of two sides of the package. The pin pitch of the Small Outline J-leaded package (SOJ) is 50 mils (1.27mm).

The number after SOJ indicates the number of pins. For example, SOJ8 means a 8-pin SOJ.

Compared to Small Outline Package (SOP), which has a gull wing (L-shaped) lead shape, Small Outline J-leaded package (SOJ), which has a J-shaped lead shape, has the advantage of less lead deformation.

In addition, those with J-shaped leads coming out of the four sides of the package are called Quad Flat J-leaded package (QFJ).

There are various types of SOJ, such as P-SOJ and C-SOJ.

Small Outline Non-leaded package (SON)

SON stands for “Small Outline Non-leaded package”.

Small Outline Non-leaded package (SON) is a package that has no leads but instead has electrode pads as connection terminals. The electrode pads protrude from two sides of the package.

Since Small Outline Non-leaded package (SON) has no leads, the package can be made almost the same size as the chip size.

In addition, those with electrode pads coming out of the four sides of the package are called Quad Flat Non-leaded package (QFN).

There are various types of SON, such as LSON and TSON.

Small Outline I-leaded package (SOI)

SOI stands for “Small Outline I-leaded package”.

Small Outline I-leaded package (SOI) is a I-leaded package with leads coming out of two sides of the package.

In addition, those with I-shaped leads coming out of the four sides of the package are called Quad Flat I-leaded package (QFI).

Small Outline F-leaded package (SOF)

SOF stands for “Small Outline F-leaded package”.

Small Outline I-leaded package (SOI) is a flat lead package with leads coming out of two sides of the package.

In addition, those with flat leads coming out of the four sides of the package are called Quad Flat F-leaded package (QFF).

Quad Flat Package (QFP)

QFP stands for “Quad Flat Package”.

Quad Flat Package (QFP) is a gull wing (L-shaped) package with leads coming out of four sides of the package.

The number after QFP indicates the number of pins. For example, QFP44 means a 44-pin QFP.

There are various pin pitches such as 1.0mm, 0.8mm, 0.65mm, 0.5mm, 0.4mm, and 0.3mm. Note that as the pin pitch becomes narrower, the lead pins bend more easily.

In addition, those with gull wing (L-shaped) leads coming out of the two sides of the package are called Small Outline Package (SOP).

There are various types of QFP, such as BQFP and GQFP.

Quad Flat J-leaded package (QFJ)

QFJ stands for “Quad Flat J-leaded package”.

Quad Flat J-leaded package (QFJ) is a J-leaded package with leads coming out of four sides of the package. The pin pitch of the Quad Flat J-leaded package (QFJ) is 50 mils (1.27mm).

QFJ (Quad Flat J-leaded package) has 18 to 84 pins.

The number after QFJ indicates the number of pins. For example, QFJ44 means a 44-pin QFJ.

Compared to Quad Flat Package (QFP), which has a gull wing (L-shaped) lead shape, Quad Flat J-leaded package (QFJ), which has a J-shaped lead shape, has the advantage of less lead deformation.

In addition, those with J-shaped leads coming out of the two sides of the package are called Small Outline J-leaded package (SOJ).

There are various types of QFJ, such as P-QFJ and C-QFJ.

Quad Flat Non-leaded package (QFN)

QFN stands for “Quad Flat Non-leaded package”.

Quad Flat Non-leaded package (QFN) is a package that has no leads but instead has electrode pads as connection terminals. The electrode pads protrude from four sides of the package.

Since Quad Flat Non-leaded package (QFN) has no leads, the package can be made almost the same size as the chip size.

In addition, those with electrode pads coming out of the two sides of the package are called Small Outline Non-leaded package (SON).

There are various types of QFN, such as LQFN and TQFN.

Quad Flat I-leaded package (QFI)

QFI stands for “Quad Flat I-leaded package”.

Quad Flat I-leaded package (QFI) is a I-leaded package with leads coming out of four sides of the package.

In addition, those with I-shaped leads coming out of the two sides of the package are called Small Outline I-leaded package (SOI).

Quad Flat F-leaded package (QFF)

QFF stands for “Quad Flat F-leaded package”.

Quad Flat F-leaded package (QFF) is a flat lead package with leads coming out of four sides of the package.

In addition, those with flat leads coming out of the two sides of the package are called Small Outline F-leaded package (SOF).

Pin Grid Array (PGA)

PGA stands for “Pin Grid Array”.

Pin Grid Array (PGA) is a package in which the pins are arranged in a grid pattern on the bottom of the package.

Pin Grid Array (PGA) pin pitch is typically 2.54mm (100 mils). Pin Grid Arrays (PGA) may have more than 400 pins.

Until the development of surface-mountable Ball Grid Array (BGA), Pin Grid Array (PGA) was the mainstream high-pin-count package for CPUs and other components used in PCs.

There are various types of PGA, such as SPGA and IPGA.

Land Grid Array (LGA)

LGA stands for “Land Grid Array”.

Land Grid Array (LGA) is a package in which the lands are arranged in a grid pattern on the bottom of the package.

Unlike Ball Grid Array (BGA), Land Grid Array (LGA) can be mounted using sockets. There are special sockets that are mounted by pressing against a kenzan-shaped electrode. Also, since the terminals of Land Grid Array (LGA) are lands, the mounting height can be reduced compared to that of Ball Grid Array (BGA).

There are various types of LGA, such as FLGA and ILGA.

Ball Grid Array (BGA)

BGA stands for “Ball Grid Array”.

Ball Grid Array (BGA) is a package in which the solder balls are arranged in a grid pattern on the bottom of the package.

There are various pin pitches such as 1.27mm, 1.0mm, 0.8mm, 0.75mm, 0.65mm, 0.5mm,and 0.4mm.

There are various types of BGA, such as FBGA and IBGA.

Other Packages

下記のパッケージを説明しました。

From now on, we will describe the packages other than those listed above.

IC Package with Tape

Dual Tape carrier Package (DTP)

DTP stands for “Dual Tape carrier Package”.

Dual Tape carrier Package (DTP) is the tape-structured package with leads coming out of two sides of the package.

Tape Automated Bonding is used to bond IC chips and TAB tape on which semiconductor integrated circuits are mounted. Packages using this method are also called Tape Carrier Package (TCP).

Quad Tape carrier Package (QTP)

QTP stands for “Quad Tape carrier Package”.

Quad Tape carrier Package (QTP) is the tape-structured package with leads coming out of four sides of the package.

IC Package containing the name CSP

Chip Size Package/Chip Scale Package (CSP)

CSP stands for “Chip Size Package/Chip Scale Package”.

Chip Scale Package (CSP) is a package that is much smaller than Ball Grid Array (BGA) and has external dimensions close to those of the semiconductor chip to be mounted.

There is no JEITA name for this type of package because it indicates its characteristics rather than its external shape.

Wafer Lebel CSP (WL-CSP)

WL-CSP stands for “Wafer Lebel CSP“.

WL-CSP is a CSP manufactured by rewiring, sealing, and external terminaling in wafer state, and finally separating and individualizing the wafers

Other IC Package

Leadless Leadframe Package (LLP)

LLP stands for “Leadless Leadframe Package”.

LLP is a type of CSP package that uses a leadframe.

It is an ultra-small and ultra-thin package, smaller than TSSOP. It was developed by National Semiconductor Corporation, and the name LLP is a registered trademark.

Dual Flatpack No-leaded (DFN)

DFN stands for “Dual Flatpack No-leaded”.

DFN has electrode pads on two or four sides of the package. DFN with electrode pads on one side are also available, but those with electrode pads on two or four sides are generally used. 4-sided DFN are also called Quad Flat Non-leaded package (QFN).

Leadless Leadframe Package (LLP) and Dual Flatpack No-leaded (DFN) are similar in structure. In Leadless Leadframe Package (LLP), the terminal pad is embedded in the package, whereas in Dual Flatpack No-leaded (DFN), a plate terminal pulled out from the side of the package is bent inward to form an electrode pad.

Multi Chip Package (MCM)

MCM stands for “Multi Chip Module”.

Multi Chip Package (MCM) is a module that contains multiple semiconductor chips and elements in a single package or module.

System in a Package (SiP)

SIP stands for “System in a Package”.

System in a Package (SiP) is a module that contains multiple semiconductor chips in a single package. The counterpart term is “System-On-a-Chip (SOC)”.

Multi Chip Package (MCM) is also a module that encapsulates multiple chips in a single package, but System in a Package (SiP) is characterized by the fact that it has some system functions in its package.

Package on a Package (PoP)

PoP stands for “Package on a Package”.

Package on a Package (PoP) is a technology to stack packages on top of packages. It enables high functionality in a small mounting area.

Package in a Package (PiP)

PiP stands for “Package in a Package”.

Package in a Package (PiP) is a technology that encapsulates the package inside the package.

Quad In-line Package (QIP / QUIP)

QIP / QUIP stands for “Quad In-line Package”.

Quad In-line Package (QIP / QUIP) is a package with alternating Dual In-line Package (DIP) legs.

A SIP with alternating legs is called a Zig-zag In-line Package (ZIP).

Thin Small Outline Circuit (TSOC)

TSOC stands for “Thin Small Outline Circuit”.

Thin Small Outline Circuit (TSOC) is a low-pin count version of Small Outline J-leaded package (SOJ).

The pin pitch is 1.27mm, the same as Small Outline J-leaded package (SOJ), but the body size is smaller.

Ceramic Flat Package (CFP)

CFP stands for “Ceramic Flat Package”.

Ceramic Flat Package (CFP) is a thin ceramic package. Structurally, it is similar to a thinner Ceramic Dual In-line Package (C-DIP).

Since it was developed at a time when surface mounting was not very popular, it can be inserted and mounted by bending the pins.

Lead Less Chip Carrier (LLCC)

LLCC stands for “Lead Less Chip Carrier”.

Lead Less Chip Carrier (LLCC) is a package with electrode pads on the ceramic surface and no lead wires.

Lead Less Chip Carrier (LLCC) is sometimes also called Quad Flat Non-leaded package (QFN).

Fan Out Wafer Level Package (FOWLP)

FOWLP stands for “Fan Out Wafer Level Package”.

Fan Out Wafer Level Package (FOWLP) is a package with external pins in an area larger than the semiconductor chip to support multiple pins.

The area of the package is larger than that of the semiconductor chip, and by extending the external pins to an area larger than the semiconductor chip, more input/output pins are secured.

Compared to Ball Grid Array (BGA), thinner and shorter wiring lengths are possible.

Chip On Board (COB)

COB stands for “Chip On Board”.

Chip On Board (COB) is a technology for mounting chips on substrates.

In Chip On Board (COB), chips are mounted on the substrate with resin, and the circuit pattern and chip electrodes are connected with pure gold wires. Compared to surface mounting of packaged products, Chip On Board (COB) enables a reduction in mounting area and a thinner profile.

Chip On Film (COF)

COF stands for “Chip On Film”.

Chip On Film (COF) is a technology to mount chips on flexible substrates.

While the mounting target of Chip On Board (COB) was a substrate, the mounting target of Chip On Film (COF) is a thin and flexible flexible flexible substrate (polyimide film substrate).

Chip On Glass (COG)

COG stands for “Chip On Glass”.

Chip On Glass (COG) is a technology to mount chips on glass substrates.

While the mounting target of Chip On Board (COB) was a substrate, the mounting target of Chip On Glass (COG) is a glass substrates.

Compared to Chip On Board (COB), Chip On Glass (COG) is more compact, but passive components cannot be mounted on glass substrates, so they must be mounted externally.

Surface Vertical Package (SVP)

SVP stands for “Surface Vertical Package”.

Surface Vertical Package (SVP) is a package with leads coming out of one side of the package, the leads are V-shaped, and the package is designed for insertion mounting.

Summary

In this article, the following information on the “Types of semiconductor (IC and transistor) packages” was explained.

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

In addition, there are various types of Transistor Outline (TO). An example is shown below.

• TO-92: Used for low-power transistors, etc.
• TO-220: Used for components with relatively high heat dissipation
• TO-247: Even larger than TO-220
• TO-3: A package used in the early days of power transistors, similar in shape to a hat.

In this article, we have tried to explain “Transistor Outline (TO) Definition” and “Types and Features of Transistor Outline (TO)” in an easy-to-understand manner using diagrams. We hope you will find it helpful.

Transistor Outline (TO) Definition

TO stands for “Transistor Outline“. Transistor Outline (TO) is a package often used for transistors, but it is also used for ICs and diodes.

There are various types of Transistor Outline (TO), which are denoted by a combination of TO and a number. For example, there are “TO-92 used for small power transistors”, “TO-220 used for components with relatively high heat dissipation”, and “TO-247, which is even larger than TO-220”.

Package materials used for Transistor Outline (TO) include plastic, metal, and ceramic.

Next, I will explain “Types and Characteristics of Transistor Outline (TO)” in turn.

TO-92

TO-92 is an insertion-mount package with a lead pitch of 1.27mm. The longer package type is called “TO-92MOD“. Alternatively, TO-92 is sometimes referred to as “TO-226AA” for JEDEC standard.

TO-92 is used for “3-terminal devices such as transistors and thyristors” and “ICs with a small number of leads such as voltage regulators”.

The main advantages of TO-92 are its low manufacturing cost and small size. However, since it cannot diffuse much heat, it cannot be used in cases where power consumption is large.

TO-252

TO-252 is a surface mountable package by forming leads. TO-252 has various names such as DPAK, PPAK, and SC-63.

The lead pitch of TO-252 is 1.27 mm.

Some manufacturers refer to the long-lead type of TO-252 as SC-64.

Like TO-92, TO-252 is used for “3-terminal devices such as transistors and thyristors” and “ICs with a small number of leads such as voltage regulators”.

TO-220・TO-202・TO-263・TO-218

Next, TO-220, TO-202, TO-263, and TO-218 with a lead pitch of 2.54 mm are explained.

TO-220

TO-220 is an insertion-mount package with a lead pitch of 2.54mm. TO-220 has a metal tab for mounting on a heat sink.

TO-220 has screw holes at the top of the package so that it can be screwed to a heat sink. Therefore, TO-220 is used for components that dissipate relatively large amounts of heat.

TO-220 has a “metal package” and a “full mold package” for the mounting part of the heat sink. In the full-molded package, the mounting part of the heat sink is covered with plastic. The full-molded product is sometimes referred to as TO-220FM.

TO-220 is available in 3-pin, 5-pin, and 7-pin versions, but the 3-pin TO-220 is most commonly used because this package is primarily used for transistors.

TO-202

TO-202 is an insertion-mount package with a lead pitch of 2.54mm.

TO-202 is characterized by a flat metal tab on the back.

TO-263

TO-263 is an insertion-mount package with a lead pitch of 2.54mm. TO-263 is shaped like a smaller metal tab of TO-220.

TO-263 has various names such as D2PAK and DDPAK.

Normally, TO-263 has formed leads to allow surface mounting.

TO-263 is available in 3-pin, 5-pin, and 7-pin versions.

TO-218

TO-218 is an insertion-mount package.

TO-218 has 2 to 5 pins. The lead pitch varies depending on the number of pins. For example, the lead pitch of 3 pins is about 5.2 mm, while that of 5 pins is 2.54 mm.

TO-218 features a flat metal tab on the back.

TO-247・TO-3P・TO-264

This section describes the TO-247, TO-3P, and TO-264 transistors, which are larger than the TO-220. The lead pitch of the TO-247, TO-3P, and TO-264 is 5.45 mm.

TO-247

TO-247 is an insertion-mount package with a lead pitch of 5.45mm.

TO-247 is a package used for components with large heat dissipation. TO-247 is similar in shape to TO-3P, which will be explained later.

TO-3P

TO-3P is an insertion-mount package with a lead pitch of 5.45mm.

TO-3P is a package used for components with large heat dissipation. TO-3P is similar in shape to TO-247.

TO-264

TO-264 is an insertion-mount package with a lead pitch of 5.45mm.

TO-264 has 2 to 5 pins.

TO-254・TO-257・TO-258・TO-259・TO-267

This section describes TO-254, TO-257, TO-258, TO-259, and TO-267, whose packages are made of metal.

TO-254

TO-254 is an insertion-mount package. The standard lead pitch of TO-254 is 3.81mm.

TO-254 has a metal body and a flat metal tab on the backside. TO-254 is more expensive than TO-220 and others due to its metal body and hermetic sealing, but it is more reliable.

TO-254 is similar in shape to the TO-257 described below, but is larger.

TO-257

TO-257 is an insertion-mount package. TO257 is packaged in a metal package with the plastic molded part of TO-220.

TO-257 is similar in shape to TO-254, but smaller than TO-254.

TO-258

TO-258 is an insertion-mount package. The standard lead pitch of TO-258 is 5.08mm.

TO-258 is similar in shape to TO-257.

TO-259

TO-259 is an insertion-mount package.

TO-259 is similar in shape to TO-258, but the metal tabs attached to the body are different.

The metal tabs attached to the TO-259 serve as heat sinks. The metal tabs also have screw holes so they can be screwed onto the heat sink.

TO-267

TO-267 is an insertion-mount package. The standard lead pitch of TO-267 is 5.08mm.

TO-3・TO-66

Next, we will discuss “TO-3, an early package of power transistors” and “TO-66, which is smaller in shape than TO-3“. Both are shaped like a hat.

TO-3

TO-3 was an early package for power transistors. Today, TO-3 is almost never used.

TO-3 is a metal package whose cylindrical part has a diameter of 22.2 mm and a height of about 5.7 mm, and its shape resembles a hat.

It is designed to be fixed to the heat sink with screws using the two holes in TO-3.

TO-3 is similar in shape to TO-66, but has a longer diameter than TO-66.

TO-66

TO-66 is a metal package whose cylindrical part has a diameter of 12.4 mm and a height of about 5.7 mm, and its shape resembles a hat.

TO-66 is similar in shape to TO-3, but has a shorter diameter than TO-3.

It is designed to be fixed to the heat sink with screws using the two holes in TO-66.

The number of pins includes 3-pin, 5-pin, and 9-pin.

TO-5・TO-33・TO-39・TO-18・TO-72・TO-46・TO-52・TO-99・TO-100・TO-8

This section describes “TO-5, TO-33, TO-39, TO-18, TO-72, TO-46, TO-52, TO-99, TO-100, and TO-8” whose packages are metallic and cylindrical in shape. These packages are rarely used today.

TO-5

TO-5 is a metal package whose cylindrical portion has a diameter of 8.1 mm and a height of about 6.3 mm.

TO-5, TO-33, and TO-39 are similar in shape. TO-5 is similar in shape to TO-18 and TO-72, but the shape of the head part is slightly different.

TO-33

TO-33 is a metal package whose cylindrical portion has a diameter of 8 mm and a height of about 2.5 mm.

TO-5, TO-33, and TO-39 are similar in shape. TO-33 is similar in shape to TO-18 and TO-72, but the shape of the head part is slightly different.

TO-39

TO-39 is a metal package whose cylindrical portion has a diameter of 8 mm and a height of about 2.5 mm.

TO-5, TO-33, and TO-39 are similar in shape. TO-39 is similar in shape to TO-18 and TO-72, but the shape of the head part is slightly different.

TO-18

TO-18 is a metal package whose cylindrical portion has a diameter of 4.7 mm and a height of about 4.8 mm.

TO-18 and TO-72 are similar in shape. TO-18 is similar in shape to TO-5, TO-33, and TO-39, but the shape of the head part is slightly different.

TO-72

TO-72 is a metal package whose cylindrical portion has a diameter of 4.7 mm and a height of about 4.8 mm.

TO-18 and TO-72 are similar in shape. TO-72 is similar in shape to TO-5, TO-33, and TO-39, but the shape of the head part is slightly different.

TO-46

TO-46 is a metal package whose cylindrical portion has a diameter of 4.7 mm and a height of about 2.4 mm.

TO-46 is slightly lower in height than TO-52.

TO-52

TO-52 is a metal package whose cylindrical portion has a diameter of 4.7 mm and a height of about 3.4 mm.

TO-52 is slightly higher in height than TO-46.

TO-99

TO-99 is a metal package whose cylindrical portion has a diameter of 8 mm and a height of about 4 mm.

The bottom of the TO-99 has 8 pins arranged in a circular pattern. In addition, there is a protrusion of about 1 mm in the center of the 8 pins to raise the bottom surface above the PCB.

TO-99 is similar to TO-100 (TO-100 has 10 pins).

TO-100

TO-100 is a metal package whose cylindrical portion has a diameter of 8 mm and a height of about 4 mm.

The bottom of the TO-100 has 10 pins arranged in a circular pattern. In addition, there is a protrusion of about 1 mm in the center of the 10 pins to raise the bottom surface above the PCB.

TO-100 is similar to TO-99 (TO-99 has 8 pins).

TO-8

TO-8 is a metal package whose cylindrical portion has a diameter of about 14 mm.

The TO-8 is available in various heights. Due to the long diameter, the cylindrical part is short.

Other TO packages

TO-126

TO-126 is a package used for “3-terminal devices such as transistors and thyristors.

Generally, a metal plate is attached to the back of TO-126, and the body has holes so that it can be screwed to a heat sink.

TO-36

TO-36 is designed to be fixed to the heat sink with screws using the hole in the center.

Summary

In this article, the following information on the “Transistor Outline (TO)” was explained.

• Transistor Outline (TO) Definition
• Types of Transistor Outline (TO)

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

Regarding the “Small Outline Diode (SOD)“, this article will explain the information below.

• Small Outline Diode (SOD) Definition
• Types of Small Outline Diode (SOD)

Small Outline Diode (SOD) Definition

SOD stands for “Small Outline Diode”. SOD is the name of the package for surface mounting of diodes.

There are various types of Small Outline Diode (SOD) such as “SOD-123“, “SOD-323F“, and “SOD-523” depending on the package size and lead shape.

In addition, there are various names for the same package shape depending on the manufacturer. For example, SOD-523 is called “EMD2” by ROHM and “SMini2-F5-B” by Panasonic.

Small Outline Diode (SOD) has the following characteristics.

Types of Small Outline Diode (SOD)

The types of Small Outline Diode (SOD) are listed in the table below. Please note that even if the package code is the same, the size, etc. may vary depending on the manufacturer, so please use this information only as a reference.

Summary

In this article, the following information on the “Small Outline Diode (SOD)” was explained.

• Small Outline Diode (SOD) Definition
• Types of Small Outline Diode (SOD)

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

Regarding the “Small Outline Transistor (SOT)“, this article will explain the information below.

• Small Outline Transistor (SOT) Definition
• Types of Small Outline Transistor (SOT)

Small Outline Transistor (SOT) Definition

SOT stands for “Small Outline Transistor”.

Since Small Outline Transistor (SOT) is a surface mount package developed for transistors, there are many 3-pin SOT. Currently, Small Outline Transistor (SOT) is used not only for transistors but also for other semiconductors (e.g., diodes) and ICs.

SOT package names differ depending on the pin pitch as shown in the figure above.

SOT-23 with a pin pitch of 0.95 mm, SOT-89 with a pin pitch of 1.5 mm, SOT-143 with a pin pitch of 1.9 mm, and SOT-223 with a pin pitch of 2.3 mm are commonly used.

Small Outline Transistor (SOT) is sometimes described with a different package code depending on the number of pins. Also, there are various designations for the same shape depending on the manufacturer.

Types of Small Outline Transistor (SOT)

The following types of SOT are described next.

• SOT-523 with a pin pitch of 0.5 mm
• SOT-323 with a pin pitch of 0.65 mm
• SOT-23 with a pin pitch of 0.95 mm
• SOT-89 with a pin pitch of 1.5 mm
• SOT-143 with a pin pitch of 1.9mm
• SOT-223 with a pin pitch of 2.3 mm

SOT-523

SOT-523 is a surface mount type package with a pin pitch of 0.5mm. SOT-523 is available in 3 to 6 pin versions.

SOT-523 may be denoted with a different package code depending on the number of pins. For example, when the middle of the SOT-523 number (“2“) becomes “4“, it is 4-pin (SOT-543), and when it becomes “5“, it is 5-pin (SOT-553).

There are various names for the same shape. For example, “SOT-523” is called “SSM” by Toshiba.

Package with a pin pitch of 0.5 mm

Also available are surface-mount type packages with a package size height of 0.55 mm and a pin pitch of 0.5 mm. These are shown below.

SOT-323

SOT-323 is a surface mount type package with a pin pitch of 0.65mm. SOT-323 is available in 3 to 6 pin versions.

SOT-323 may be denoted with a different package code depending on the number of pins. For example, when the middle of the SOT-323 number (“2“) becomes “4“, it is 4-pin (SOT-343), and when it becomes “5“, it is 5-pin (SOT-353).

Flat leaded products have an “F” at the end. For example, a 4-pin flat leaded product is “SOT-343F“.

There are various names for the same shape. For example, “SOT-323” is called “USM” by Toshiba.

Package with a pin pitch of 0.65 mm

In addition, no-lead surface-mount type packages with a pin pitch of 0.65 mm are also available. These are shown below.

SOT-23

SOT-23 is a surface mount type package with a pin pitch of 0.95mm. SOT-23 is available in 3 to 6 pin versions.

SOT-23 may be denoted with a different package code depending on the number of pins. For example, 5-pin package may be referred to as “SOT-23-5” or “SOT-25“.

There are various names for the same shape. For example, “SOT-23-3” is called “S-Mini” by Toshiba.

Note that “SOT-23” and “SOT23-3” are 3-pin surface-mount type packages with a pin pitch of 0.95 mm, but the size may be 2.9 x 2.4 x 1.0 or 2.9 x 2.8 x 1.1.

Package with a pin pitch of 0.95 mm

SOT-89

SOT-89 is a surface mount type package with a pin pitch of 1.5mm. SOT-89 is available in 3-pin and 5-pin versions (3-pin is more common).

SOT-89 may be denoted with a different package code depending on the number of pins. For example, 5-pin package may be referred to as “SOT-89-5“.

There are various names for the same shape. For example, “SOT-89” and “SOT-89-3” are called “MPT3” in ROHM.

Package with a pin pitch of 1.5 mm

SOT-143

SOT-143 is a surface mount type package with a pin pitch of 1.9mm. SOT-143 has 4 pins.

Only one pin is wider than the others.

There are various names for the same shape. For example, “SOT-143” is called “Mini4-G4-B” by Panasonic.

Package with a pin pitch of 1.9 mm

SOT-223

SOT-223 is a surface mount type package with a pin pitch of 2.3mm. SOT-223 is available in 4 to 8 pin versions.

The 4-pin SOT-223-5 has a pin pitch of 2.3 mm. 5-pin “SOT-223-5” has five legs coming out of one side of the package, resulting in a pin pitch of 1.27 mm. 8-pin “SOT-223-8” has four legs coming out of both sides of the package, resulting in a pin pitch of 1.53 The pin pitch is 1.53mm.

Package with a pin pitch 2.3mm (← 4-pin only)

The “SOT-428” package, which is a formed SC-64 (TO-251) to allow surface mounting, also has a pin pitch of 2.3 mm. It is shown below.

Other Packages

In addition to the packages described so far, there are others that start with SOT. They are listed below.

Summary

In this article, the following information on the “Small Outline Transistor (SOT)“ was explained.

• Small Outline Transistor (SOT) Definition
• Types of Small Outline Transistor (SOT)

Thank you for reading.

Copyright © 2026 Electrical Information All Rights Reserved.

Regarding the “Land Grid Array (LGA)“, this article will explain the information below.

• Land Grid Array (LGA) Definition
• Types of Land Grid Array (LGA)

Land Grid Array (LGA) Definition

LGA stands for “Land Grid Array”.

Land Grid Array (LGA) is a package in which the lands are arranged in a grid pattern on the bottom of the package.

Land Grid Array (LGA) is suitable for high-speed and high-frequency operation because of its small terminal parasitic inductance.

Unlike Ball Grid Array (BGA), Land Grid Array (LGA) can be mounted using sockets. There are special sockets that are mounted by pressing against a kenzan-shaped electrode.

Also, since the terminals of Land Grid Array (LGA) are lands, the mounting height can be reduced compared to that of Ball Grid Array (BGA).

The “package mounting height”, “pin pitch”, etc. change depending on the English letter in front of the LGA.

For example, “L” means that the package installation height L is “1.20mm < L ≤ 1.70mm”. Therefore, “LLGA” with “L” in front of LGA means LGA with a package installation height of “1.20mm < L ≤ 1.70mm”.

Types of Land Grid Array (LGA)

FLGA

The “F” in front of LGA stands for “Fine pitch“.

The “F” makes the pin pitch shorter as shown below.

Therefore, “Fine-pitch Land Grid Array (FLGA)” means LGA with a pin pitch of 0.8 mm or less.

ILGA

The “I” in front of LGA stands for “Interstitial.

Therefore, “Interstitial Land Grid Array (ILGA)” means LGA with package terminals that are not grid-shaped (e.g., staggered pattern).

LLGA

The “L” in front of LGA means that the package installation height L is “1.20mm < L ≤ 1.70mm“.

Therefore, “Low-Profile Land Grid Array (LLGA)” is a LGA with a package installation height of “1.20mm < L ≤ 1.70mm”.

LFLGA

The “L” in front of FLGA means that the package installation height L is “1.20mm < L ≤ 1.70mm“.

Therefore, “Low-Profile Fine-pitch Land Grid Array (LFLGA)” is a FLGA with a package installation height of “1.20mm < L ≤ 1.70mm”.

TLGA

The “T” in front of LGA means that the package installation height T is “1.00mm < T ≤ 1.20mm“.

Therefore, “Thin Land Grid Array (TLGA)” is a LGA with a package installation height of “1.00mm < T ≤ 1.20mm”.

TFLGA

The “T” in front of FLGA means that the package installation height T is “1.00mm < T ≤ 1.20mm“.

Therefore, “Thin Fine-pitch Land Grid Array (TFLGA)” is a FLGA with a package installation height of “1.00mm < T ≤ 1.20mm”.

VLGA

The “V” in front of LGA means that the package installation height V is “0.80mm < V ≤ 1.00mm“.

Therefore, “Very thin Land Grid Array (VLGA)” is a LGA with a package installation height of “0.80mm < V ≤ 1.00mm”.

VFLGA

The “V” in front of FLGA means that the package installation height V is “0.80mm < V ≤ 1.00mm“.

Therefore, “Very thin Fine-pitch Land Grid Array (VFLGA)” is a FLGA with a package installation height of “0.80mm < V ≤ 1.00mm”.

WLGA

The “W” in front of LGA means that the package installation height W is “0.65mm < W ≤ 0.80mm“.

Therefore, “Very-Very thin Land Grid Array (WLGA)” is a LGA with a package installation height of “0.65mm < W ≤ 0.80mm”.

WFLGA

The “W” in front of FLGA means that the package installation height W is “0.65mm < W ≤ 0.80mm“.

Therefore, “Very-Very thin Fine-pitch Land Grid Array (WFLGA)” is a FLGA with a package installation height of “0.65mm < W ≤ 0.80mm”.

ULGA

The “U” in front of LGA means that the package installation height U is “0.50mm < U ≤ 0.65mm“.

Therefore, “Ultra-thin Land Grid Array (ULGA)” is a LGA with a package installation height of “0.50mm < U ≤ 0.65mm”

UFLGA

The “U” in front of FLGA means that the package installation height U is “0.50mm < U ≤ 0.65mm“.

Therefore, “Ultra-thin Fine-pitch Land Grid Array (UFLGA)” is a FLGA with a package installation height of “0.50mm < U ≤ 0.65mm”

XLGA

The “X” in front of LGA means that the package installation height X is “X ≤ 0.50mm“.

Therefore, “Extra thin Land Grid Array (XLGA)” is a LGA with a package installation height of “X ≤ 0.50mm”

XFLGA

The “X” in front of FLGA means that the package installation height X is “X ≤ 0.50mm“.

Therefore, “Extra thin Fine-pitch Land Grid Array (XFLGA)” is a FLGA with a package installation height of “X ≤ 0.50mm”

HLGA

The “H” in front of LGA stands for “Heat sink“.

Therefore, “LGA with Heat sink (HLGA)” means a “LGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

HLLGA

The “H” in front of LLGA stands for “Heat sink“.

Therefore, “HLLGA” means a “LLGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

HTLGA

The “H” in front of TLGA stands for “Heat sink“.

Therefore, “HTLGA” means a “TLGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

HVLGA

The “H” in front of VLGA stands for “Heat sink“.

Therefore, “HVLGA” means a “VLGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

HWLGA

The “H” in front of WLGA stands for “Heat sink“.

Therefore, “HWLGA” means a “WLGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

HULGA

The “H” in front of ULGA stands for “Heat sink“.

Therefore, “HULGA” means a “ULGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

HXLGA

The “H” in front of XLGA stands for “Heat sink“.

Therefore, “HXLGA” means a “XLGA with Heat sink“. A heat-dissipating surface called a thermal pad is provided on the board mounting side surface.

P-LGA

The “P-” in front of LGA stands for “Plastic“.

Therefore, “Plastic LGA (P-LGA)” means a “LGA whose package material is plastic“.

C-LGA

The “C-” in front of LGA stands for “Ceramic“.

Therefore, “Ceramic LGA (C-LGA)” means a “LGA whose package material is ceramic“.

S-FLGA

The “S-” in front of FLGA stands for “Silicon“.

Therefore, “Silicon FLGA (S-FLGA)” means a “FLGA whose package material is silicon“.

Summary

In this article, the following information on the “Land Grid Array (LGA)“ was explained.

• Land Grid Array (LGA) Definition
• Types of Land Grid Array (LGA)

Thank you for reading.

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