A.C. Characteristics of Op-amp

A.C. Characteristics of Op-amp

The important a.c. characteristics of op-amp are,

1. Slew rate 2. Frequency response

The slew rate is already discussed. It indicates the ability of op-amp with which it can change its output according to changes in the input.

1. Frequency Response of Op-amp

Ideally, an op-amp should have an infinite bandwidth. This means the gain of op-amp must remain same for all the frequencies from zero to infinite. Uptill now we have assumed gain of the op-amp as constant but practically op-amp gain decreases at higher frequencies. Such a gain reduction with respect to frequency is called roll off.

This happens because gain of the op-amp depends on the frequency and hence mathematically it is a complex number. Its magnitude and the phase angle changes with the frequency. The plot showing the variations in magnitude and phase angle of the  gain due to the change in frequency is called frequency response of the op-amp. In such plots, to accommodate large range of frequency, it is plotted on a logarithmic scale. The gain magnitude can be plotted as a numerical value or may be expressed in decibels. When the gain in decibels, phase angle in degrees are plotted against logarithmic scale of frequency, the plot is called Bode plot. The manner in which the gain of the op-amp changes with variation in frequency is known as the magnitude plot and the manner in which the phase shift changes with variation in frequency is known as the phase angle plot. Generally magnitude plot is supplied by the manufacturers.

The dependence of gain of the op-amp on frequency is basically because of presence of capacitive component in the equivalent circuit of the op-amp. As op-amp uses BJT and FET, which have the junction capacitances which is very small. But at high frequency, these offer decreased reactance. Not only the BJT and FET, but the construction of op-amp also contributes to the presence of capacitance. All the resistors and transistors in op-amp are fabricated on an insulator. Similarly there are conducting material wires, connecting the various components. The two conductors separated by an insulator produces capacitive effect. Hence overall there exists a capacitive effect in the op-amp.

To obtain the frequency response, consider the high frequency model of the op-amp with a capacitor C at the output, taking into account the capacitive effect present. It is shown in the Fig. 2.15.1.

Let - jXC be the capacitive reactance due to the capacitor C. From the Fig. 2.15.1, using voltage divider rule, 

Hence the open loop voltage gain as a function of frequency is

where A_OL (f) = Open loop voltage gain as a function of frequency

A_OL = Gain of op-amp at 0 Hz i.e. d.c.

f = Operating frequency

f_o = Break frequency or cut off frequency of op-amp

For a given op-amp and selected value of C, the frequency fo is constant. The equation (2.15.5) can be written in the polar form as

At f = 0 Hz, the magnitude is A_OL , while ϕ (f) = 0°

For IC 741 op-amp, f_o = 5 Hz and the open loop gain 200,000, we can calculate gain and phase shifts at various frequencies as shown in Table 2.15.1.

As the frequency increases till f_o, the gain is almost constant but after f_o, the gain reduces with a rate of -20 dB/decade. The maximum possible phase shift is -90°. Hence the frequency response is shown as in the Fig. 2.15.2.

The following observations can be made from the frequency response of an op-amp:

i) The open loop gain A_OL is almost constant from 0 Hz to the break frequency f 0.

ii) At f = f0, the gain is 3 dB down from its value at 0 Hz. Hence the frequency f0 is also called as - 3 dB frequency. It is also known as comer frequency.

iii) After f = f₀, the gain A_OL(f) decreases at a rate of 20 dB/decadeor6 dB/octave. A decade is 10 times change in frequency while octave is 2 times change in frequency. As gain decreases, slope of the magnitude plot is - 20 dB/decade or - 6 dB/octave, after f = f_o.

iv) At a certain frequency, the gain reduces to 0 dB. This means 20 log | A_OL(f)| is 0 dB i.e. | A_OL(f) | = 1. Such a frequency is called gain cross-over frequency or unity gain bandwidth (UGB). It is also called closed loop bandwidth. UGB is the gain bandwidth product only if an op-amp has a single break frequency, before AOL(f) dB is zero. IC 741 op-amp has a single break frequency and its UGB is approximately 1 MHz. So for an op-amp with single break frequency f0, after fo the gain bandwidth product is constant equal to UGB.

UGB = A_OLf_o … (2.15.8)

UGB is also called gain bandwidth product and denoted as ft. Thus ft is product of gain of op-amp and bandwidth.

The break frequency is nothing but a corner frequency f 0. At this frequency, slope of the magnitude plot changes. The op-amp for which there is only once change in the slope of the magnitude plot, is called as single break frequency op-amp. The IC 741 op-amp, is single break frequency i.e. slope of the plot changes only once from 0 to -20 dB/decade at f0, as shown in the Fig. 2.15.2.

But for a single break frequency we can also write

UGB = A_f f_f   … (2.15.9)

where          A_f = Closed loop voltage gain

f_f = Bandwidth with feedback

So with feedback, at any point after the break frequency on frequency response, product of gain and frequency is constant equal to UGB. Remember that this is applicable only for op-amps with single break frequency like op-amp IC 741.

v) The phase angle of an op-amp with a single break frequency varies between 0° to 90°. The maximum possible phase shift is - 90°, i.e. output voltage lags input voltage by 90° when phase shift is maximum.

vi) At a comer frequency f - fo, the phase shift is - 45°.

For a typical op-amp, in a data sheet the value of UGB is given instead of the value of the break frequency f_o. Therefore fo can be calculated as

f_o = UGB / A_OL … ( 2.15.10)

However, in a practical op-amp there are number of stages. Each stage introduces a capacitive component. Thus there are number of different break frequencies. But op-amp like 741 is internally compensated and has only one break frequency.

Review Questions

1. List the a.c. characteristics of op-amp and define each of them.

May-07,08,13, Dec.-09, 16, Marks 4

2. Write a technical note on frequency response characteristics of op-amp.

Dec.-09,10, May-16, Marks 8