# How does Antilog amplifier using Diode work?

An antilog amplifier using a diode is a type of electronic circuit that amplifies the logarithm of an input signal, and then applies the inverse function (the antilogarithm) to produce an output signal. Here Antilog amplifier is explained, designed and equation derived. An antilog amplifier is an electronics circuit that outputs exponential of the input signal. Antilog amplifier can be designed using operational amplifier and diode or transistor. Here antilog amplifier with diode is explained. Diodes and transistors are non-linear components and therefore antilog amplifier is one example of non-linear application of operational amplifier. Log and antilog amplifier are used for mathematical operations like division, multiplication, square root calculation, power extraction, true rms conversion etc.

The basic circuit of an antilog amplifier using a diode consists of a diode at the inverting input of an op-amp and a feedback resistor back to the inverting input of the operational amplifier. The diode is typically a signal diode, such as a 1N4148 or a 1N914. The operational amplifier amplifies the difference between the input voltage and the voltage across the diode, which is the logarithm of the input voltage. The feedback capacitor helps to stabilize the circuit. The output of the operational amplifier is then passed through a circuit that applies the inverse function, the antilogarithm, to produce the final output signal. This is typically done using a transistor or another operational amplifier.

Overall, the antilog amplifier using a diode takes an input signal and amplifies it in a logarithmic way, and then applies the antilogarithm function to produce the output signal, making it useful for a variety of applications such as in audio, signal processing and telecommunications.

### Basic Antilog amplifier with Diode

The following shows the circuit diagram of basic antilog amplifier with diode.

In the above antilog amplifier circuit diagram, the input signal is applied to the non-inverting input of the operational amplifier, the non-inverting input is grounded and the output is taken from op-amp output. The diode creates a voltage drop across it, which is dependent on the current flowing through it. This voltage drop creates a logarithmic relationship between the input current and the voltage across the diode.

In the circuit, Vin is the input signal and Vout is the output signal. We can show that the output voltage Vout is exponential of the input voltage as follows.

In the circuit, we can see that the node A is grounded and hence the node B is virtually grounded. Applying KVL on the output side we can write,

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

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

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

The current through the feedback resistor $$R_{f}$$ is,

$$I_{f} = I_{0} e^{\frac{V_{in}}{ \mu V_{T}}}$$

Therefore the output voltage is given by,

$$V_{out} = - I_{0} R_{f} e^{\frac{V_{in}}{ \mu V_{T}}}$$

Let   $$V_{ref} = I_{0} R_{f}$$ then,

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

This antilog amplifier equation shows that the output is anti-log or exponential of the input signal.

### Antilog amplifier design

The following shows circuit diagram of antilog amplifier designed with LM358 operational amplifier and 1N4148 switching diode.

Consider an input sine wave of 1V amplitude and frequency of 1KHz. Then the input and output waveform of the antilog amplifier is shown below.

#### Recommedations

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- How does Log Amplifier using transistor work?