# What is Miller Effect : Effect of Miller Capacitance

We know that in all the electrical and electronic circuits, the capacitor has unique importance. Such an effect of the capacitors can be analyzed by the frequency response. This means the effect of capacitance at lower and higher frequencies and their reactance can be easily analyzed with the frequency responses. Here we are discussing the important term which is called **miller effect in amplifiers**, and its definition and effect of miller capacitance.

## What is the Miller Effect?

The miller effect name is taken from the work of John Milton miller. With the help of miller theorem, the capacitance of the equivalent circuit of the inverting voltage amplifier can be increased by placing extra impedance between input and output terminals of the circuit. Miller theorem states that a circuit having an impedance (Z), connecting between two nodes where the voltage levels are V1 and V2.

When this impedance is replaced by two different impedance values and connected to the same input & output terminals to the ground for analyzing the frequency response of the amplifier as well as to increase the input capacitance. Such an effect is called a Miller effect. This effect occurs only in inverting amplifiers.

### Effect of Miller Capacitance

This effect protects the capacitance of the equivalent circuit. At higher frequencies, the circuit gain can be controlled or reduced by the miller capacitance because handling the inverting voltage amplifier at such frequencies is a complex process.

If there is some capacitance between the input & output of an inverting voltage amplifier then it will appear to be multiplied by the gain of the amplifier. The additional amount of capacitance will be due to this effect so it is called Miller capacitance.

The below figure shows the ideal inverting voltage amplifier and Vin is the input voltage and Vo is the output voltage, Z is the impedance, the gain is indicated by –Av. And output voltage **Vo = -Av.Vi**

Here, the ideal inverting voltage amplifier attracts zero current and all the current flows through impedance Z.

Then, current** I=Vi-Vo/Z**

**I=Vi(1+Av)/Z**

The input impedance **Zin=Vi/Ii = Z/1+Av**.

If Z represents the capacitor with impedance, then** Z =1/sC.**

Therefore input impedance **Zin = 1/sCm**

Here **Cm = C (1+Av)**

Cm-miller capacitance.

### Miller Effect in IGBT

In the IGBT (insulated gate bipolar transistor), this effect will be occurred because of its structure. In the below IGBT equivalent circuit, two capacitors are in series form.

The first capacitor value is fixed and the second capacitor value is dependent on the width of the drift region area & collector-emitter voltage. So, any changes in Vce that causes a displacement current through miller capacitance. Common base & common collector amplifiers are not going to feel the effect of the miller. Because in these amplifiers, one side of the capacitor (Cu) is connected to the ground. This helps to take it out from the effect of the miller.

Thus, this effect is mainly used to increase the circuit capacitance by placing impedance between input and output nodes of the circuit. Then an additional capacitance treated as miller capacitance. Miller’s theorem is applicable to all three-terminal devices. In FET’s also the gate to drain capacitance can be increased by this effect. But it can be a problem in broadband circuits. As the capacitance increases the bandwidth is going to be reduced. And in narrowband circuits, the miller effect is a little less. This needs to be improved by some modifications.