# How does Antilog Amplifier with Transistor work?

Antilog amplifier is electronic circuit that produces antilog or exponential of input signal. An antilog amplifier can be designed using operational amplifier and either a diode or a transistor. Here antilog amplifier design using transistor is explained with LM358 op-amp and 2N3904 transistor. Antilog amplifier design with diode was explained in the previous tutorial how does Antilog amplifier using Diode work?.

### Basic Antilog Amplifier with Transistor

The circuit diagram of a basic antilog amplifier with transistor is shown below.

In the above circuit, a PNP transistor is placed at the input of the inverting terminal. A resistor is placed in the feedback path. The output signal Vout is the exponential of the input signal Vin which is derived as follows.

Applying KVL in the output circuit we have,

$$V_{out} = V_{2} - I_{f} R_{f}$$

The current through the feedback resistor $$I_{f}$$ is also the collector current $$I_{c}$$, so $$I_{f}$$ = $$I_{c}$$.

Since $$V_{2} = 0$$ due to virtual ground,

$$V_{out} = - I_{c} R_{f} --------------(1)$$

The collector current $$I_{c}$$ is given by,

$$I_{c} = I_{s} ( e^{\frac{V_{BE}}{ V_{T}}} - 1)$$

Since $$e^{\frac{V_{BE}}{ V_{T}}} >> 1$$

$$I_{c} = I_{s} e^{\frac{V_{BE}}{ V_{T}}}$$

Since that $$V_{BE} = V_{in}$$,

$$I_{c} = I_{s} e^{\frac{V_{in}}{ V_{T}}}$$

Therefore the output voltage in equation(1) is given by,

$$V_{out} = - I_{s} R_{f} e^{\frac{V_{in}}{ V_{T}}}$$

Let   $$V_{ref} = I_{s} R_{f}$$ then,

$$V_{out} = - V_{ref} e^{\frac{V_{in}}{ V_{T}}}$$

Thus the output voltage  $$V_{out}$$ is proportional to the exponential of input voltage $$V_{in}$$.

The following is circuit diagram of antilog amplifier designed with LM358 operational amplifier and 2N3904 transistor.

The following shows waveform of input and output signal from the antilog amplifier designed with transistor when the input signal is a sine wave of 1V with frequency of 1KHz.

In this tutorial we explained how the antilog amplifier with transistors work. The following are tutorials that shows how log amplifier works with diode and transistors.