Concept of Frequency Compensation used in operational amplifiers

Concept of Frequency Compensation

May-03, 04, 09, 16, Dec.-06

It is seen earlier that the op-amp circuit with single break or comer frequency is inherently stable. 

Consider the system with three break or corner frequencies. This is possible in practice due to the capacitive component produced by the various number of stages.

The open loop frequency dependent transfer function of such a system can be assumed as,

where A_OL = gain at 0 frequency or d.c. gain and w1, 2, 3 are the corner frequency values such that 0 < ω₁ < ω₂ < ω₃·

The phase shift introduced by such loop gain is,

Hence at high frequencies ϕ (f) → - 270°.

Thus the phase shifts of each stage θ₁, θ₂ and θ₃ add together to give the total phase shift of op-amp where,

At f = f₁, θ₁ = 45° while θ₂ and θ₃ are negligible. At f = f₂, 01 is almost - 90° as θ₁ f₂ > f₁ and θ₂ = -45°. Thus the total phase shift becomes - 135°. The θ₃ is still small. At θ₁ 90° as f₃f₂> f₁ while 03 reaches to - 45°. Thus the total phase shift becomes 90° - 90° - 45° = - 225°.

This is the additional phase shift to – 180° phase shift which is present between inverting terminal and output terminal.

Due to such additional phase shift op-amp may behave oscillatory and circuit becomes unstable. This is shown in the Fig. 2.32.1.

Thus as seen from the frequency response of noncompensated op-amp, due to additional phase shift, at ω = ω_gc, there is chance that total phase shift becomes almost - 360° and circuit becomes unstable. The phase margin is negative in such a case.

To build the oscillations the total phase shift need not be exactly - 360° but if it is more than - 315° and A_OL β > 1 then oscillations may start.

To avoid the oscillations, the total phase shift should not be greater than - 315° i.e. due to the op-amp, excluding -180° between inverting terminal and output, the phase shift should not be greater than - 315° + 180° = -135°

Minimum phase margin = 180° - 135° = + 45°

Thus for op-amp circuit stability, it is necessary to have phase margin of + 45°.

This is possible by providing necessary compensation so that only one breakover frequency exists.

Due to this, phase shift of op-amp cannot increase beyond - 90°. Thus there is no chance that Op-amp phase shift becomes -135° and phase margin is automatically more than + 45°.

This technique of compensation is called frequency compensation technique. Using this technique, the op-amp is converted to single break frequency op-amp. The frequency response of such op-amp has only one roll off rate of -20 dB/dec and is as shown dotted in the Fig. 2.32.1. 

Key Point The method of modifying loop gain frequency response of the op-amp so that it behaves like single break frequency response which provides sufficient positive phase margin is called frequency compensation technique.

Op-amp circuits with high closed loop gain are early to compensate while op-amp circuits with low closed loop gain are difficult from compensation point of view to provide stability.

When a lower closed loop gain and large bandwidth is required for a system, suitable compensation technique is used.

The two types of compensation techniques are used in practice namely, i) External compensation ii) Internal compensation.

Review Question

1. Explain on frequency compensation used in operational amplifiers.

May-03, 04, 16, Marks 12, Dec.-06, Marks 10, May-09, Marks 8