Frequency Response of Op-amp – An Introduction

The frequency response of amplifier refers to the band of frequencies or frequency range that the amplifier was designed to amplify.

Frequency Response of the op-amp: In open loop configuration, the gain of the op–amp is not constant and varies with the frequency and the product of gain and frequency remains constant till the unity gain frequency for the op–amp, which is known as the gain bandwidth product of the op–amp.

Gain – Bandwidth Product:

It is the bandwidth of the op-amp when the voltage gain is 1.

For 741: 1MHz (approx.)

Also called as:

• Closed loop bandwidth or
• Unity gain bandwidth or
• Small signal bandwidth

Equivalent Circuit of Op-Amp

 

• Op-amp can be modelled as Voltage Controlled Voltage Source (VCVS)
• Av_id = equivalent Thevenin voltage source
• R_o = Thevenin equivalent resistance looking back into the output terminal of op-amp
• V_o = Av_id = A (V₁ – V₂)
• v_id = Difference between voltage at non-inverting & inverting terminals
• Output voltage is proportional to the algebraic difference between the two input voltages.
• Polarity of the output voltage depends on polarity of difference between non-inverting and inverting input terminals

Ideal Voltage Transfer Curve

• Curve is almost vertical because of very large gain A
• Slope of the voltage transfer characteristic curve gives gain.

Frequency Response of Op-Amp

• Ideally infinite bandwidth

• This means ideally op-amp amplifies all the frequency with equal gain.
• But ideally gain depends on frequency

Gain depends on frequency because of capacitive components which are present due to:

• Junction Capacitance of FET & BJT at high frequencies
• Construction of op-amp using FET and MOSFET which forms MOS capacitance
• Interconnects used to connect different stages

These capacitance also limits the maximum frequency of operation of op-amp which is given by the slew rate.

To model all these capacitances in ideal model, we connect a capacitor at the output.

Practical Equivalent Model of Op-Amp:

Using Voltage Division:

Output voltage can be written as

Substituting the values

f = Operating frequency

From 0 Hz to f₀

• Open loop gain is almost constant from 0 Hz to cutoff frequency f

At f = f₀

• The voltage gain falls to 1/√2 times the initial value
• Power at this frequency falls to ½ times the maximum power.
• This is also called as 3 dB down frequency.

After f = f_o

• The gain decreases at 20 dB/decade or 6 dB/octave

From the Plot:

This frequency is called as Gain Cross Over frequency or Unity Gain Bandwidth of op-amp.

Gain Bandwidth Product of the-op amp is constant.

This means as the gain of the op-amp decreases, its cutoff frequency increases.

Ques. An op-amp has a closed loop gain of 40 dB and unity gain frequency of 1 MHz. The cutoff frequency of the op-amp is:

1. 1 kHz
2. 1 MHz
3. 10 kHz
4. 10 MHz

Ans. c

Solution:

A_CL = 40 dB = 100

f_u = GBP = 1MHz = 10⁶ Hz

f_u = ?

Since the gain bandwidth product is constant

A_CL × fc = G.B.P.

741 IC PIN-Diagram

• 8 Pin IC
• Pin 1 & 5 offset null pins.
• Pin 2 is inverting Input (V^–)
• Pin 3 is non-inverting Input (V⁺)
• Pin 4 is – V_EE supply
• Pin 6 is for Output
• Pin 7 is + V_cc supply
• Pin 8 is not connected and not used

741 IC derives its name:7 → Number of pins used4 → Number of inputs (inverting, non-inverting, +V_cc and -V_EE)1 → Number of outputs (only 1)Use of Offset Null Pins: DC Voltage at output when both input terminals are ground is called as output offset voltage.Output Offset Voltage Reasons

• Input bias current
• Input offset current
• Input offset voltage

The figure below shows the compensation technique to make the output offset voltage zero.Both the inputs of the op-amp are grounded and a 10k potentiometer is connected between the two offset null pins, the position of viper on potentiometer is adjusted till the output offset voltage becomes zero.