## Introduction: How to Measure the Small Signal Characteristics of a BJT

A bipolar junction transistor, or BJT, is a type of transistor. They are commonly found in electronic amplifier circuits such as those used to transmit data wirelessly, and in radios.

The above image is a schematic of a BJT. C is the Collector, B is the Base, and E is the Emitter.

The internal characteristics of a BJT can vary with temperature, voltage, and current. Because of this, before putting a transistor into your project or device you may want to measure the internal characteristics of the transistor at the voltage and current you will have it operating.

This Instructable shows you how to calculate the small signal characteristics of a BJT using what is called the hybrid-pi model, and by taking measurements of the currents going into the BJT. These characteristics are called the transconductance, current gain, and internal resistance.

To perform the steps in this Instructable, you need to be able to perform some fairly basic math, as well as know what voltage and current are.

Supplies needed:

- Pencil and paper
- Calculator
- Resistors and transistor
- Multimeter

To measure these values, you need to take the following steps:

- Create a circuit to test your transistor in.
- Measure the voltage or current going into the transistor.
- Calculate the Beta value (current gain at low frequencies) and the transconductance.
- Using the values calculated for current gain and transconductance, find R-π, the internal resistance.

**An important safety note: If the current through the transistor is too high, it may melt or explode. For most small transistors, anything close to an amp of current is high.**

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## Step 1: Set Up a Test Circuit

To test the collector and base currents you will first need to set up a circuit to test them in. Because BJTs usually operate at very low currents, we attach 1000 ohm resistors on each node of the transistor to ensure that the transistors are not damaged.

The above image shows the diagram for the a test circuit. It uses a 2n3904 BJT (labeled Q1 in the diagram), using 1000 ohm resistors (R1, R2, R3) on each terminal, with 15 volts on the collector terminal and 2 volts on the base terminal.

## Step 2: Measure the Voltage Across the Resistors

Because BJTs operate at such low current, instrument noise can make it difficult to accurately measure the current. Instrument noise is small, random variations in the measured values. In most multimeters, this is a very small amount, but it is similar in magnitude to the currents in the test circuit. In order to compensate for this issue, you may instead want to measure the voltage across the resistors and then use Ohm's law to calculate the current.

Ohm's law states the the voltage across a component equals the current through it multiplied by its resistance: V = I * R. To find the current through the resistors divide the voltage by the resistance: I = V / R.

__Test Circuit:__

The pictures shown above show the values you would measure if you constructed the test circuit. The voltage on the collector resistor is **1.359 volts**, and the voltage on the base resistor is **8.107 millivolts.**

Because the resistors in the test circuit are all 1000 ohms, dividing by the resistance simply changes the prefix to the one below it on the SI scale: **1.359 volts** on the collector becomes **1.359 milliamps **through the collector, and **8.107 millivolts **on the base becomes **8.107 microamps **through the base.

## Step 3: Calculate the Internal Characteristics Based on Input Currents

Now that you've calculated the internal currents you can calculate the small signal values of the BJT.

These are as follows:

β0: Current Gain

This value represents the ratio between the current into the collector and the current into the base. The particular value is specific to each transistor, and can also vary with temperature.

gm: Transconductance

This value represents the ratio between the current out of the transistor and the voltage into it. V is thermal voltage, which is a constant equal to 26 millivolts at room temperature.

rπ: Internal Resistance

This value is the resistance between the base and emitter terminals of the transistor. Like current gain, it is unique to each transistor.

## Step 4: Calculate Current Gain

To calculate current gain, divide the value of the current going into the base terminal by the value of the current going into the collector terminal.

This value represents how much the transistor amplifies the current going into the collector terminal. It is just a number, with no units. However, to make it easier to understand what it is doing, you may find it useful to write this value as amps per amps.

__Test Circuit:__

For the test circuit the collector current is **1.359 milliamps, **and the base current is **8.107 microamps.** Dividing the collector current by the base current gives a current gain of **167.6 amps per amp.**

## Step 5: Calculate Transconductance

Transconductance is an intimidating word, but it is just the ratio between the voltage into the transistor and current out of the transistor.

To calculate it, divide the current into the collector terminal by VT, thermal voltage. Doing so gives you a value in **inverse ohms**, written as **mhos. **

__Test Circuit:__

For the test circuit the collector current is** 1.359 milliamps.** The thermal voltage is constant at **26 millivolts. **This results in a value of **52.27 millimhos.**

## Step 6: Calculate Internal Resistance

The last step is to calculate the internal resistance of the BJT. This value represents how much of the voltage placed on the collector terminal makes it to the emitter terminal.

To calculate it, divide the value of current gain by the transconductance, both calculated in previous steps. This calculation gives you a result in ohms.

__Test Circuit:__

For the test circuit the current gain is **167.6 amps per amp, **and the transconductance is **52.27 milliohms. **Performing the calculation gives a result of **3207 ohms.**

## Step 7: Conclusions

After having gone through these steps, you will have calculated the main internal characteristics of whatever BJT you were testing. Keep in mind that these values are only valid for lower frequencies, and will change at high frequencies.

One thing you may have noticed after going through these steps is that you did not calculate Ro. This value is the output resistance due to the Early effect, and changes depending on the voltage and is unique to each transistor. If you want to find out what it is, you will need to look it up in the datasheet for your transistor.

Learn more about the Early effect

If you're interesting in learning more about the future of computing without transistors, you may find these interesting:

## Discussions

3 years ago

Great Tutorial. Thanks for sharing.