OPERATIONAL AMPLIFIERS

AC CHARACTERISTICS

Frequency Response• Ideal Op-Amp will have Infinite Gain• In general, open loop gain is 90dB with dc signal• What should be the expected gain for audio and

other high frequency signal?– Must be same, but practically it is not possible– Op-Amp gain decreases (or roll-off) at higher frequencies

• What Causes the gain of the op-amp to roll off?– Presence of capacitive component !!!• Internal construction of op-amp & physical characteristics of

the device

High frequency Model of the Op-Amp• HF model of the op-amp with only one corner

frequency– One pole due to RoC & -20dB/decade roll-off

• The open loop gain of the op-amp with only one corner frequency is

• Where f1 is the corner frequency or the upper 3-dB frequency of the op-amp.

• From the magnitude & phase characteristics, it can be seen that– for f << f1, the

magnitude of the gain is 20 log AOL in dB

– for f = f1, the gain is 3dB down from the dc value of AOL , called corner frequency.

– for f >> f1, the gain rolls-off at the rate of -20 dB/decade or – 6 db/octave.

• From the phase characteristics– Phase angle is zero at f = 0– At f1, the phase angle is -45o

(lagging) and

– Infinite frequencies, the phase angle is -90o.

• For single RC pair, maximum phase change of 90o can occur.

• The voltage transfer function in s-domain can be written as

• For number of stages or RC pole pairs, there will be number of corner frequencies

Stability of Op-Amp• What is the effect of feedback on op-amp?• Resistor in the feedback part of the op-amp• For inverting amplifier, 180o phase shift in the

output, at low frequencies

• The closed loop transfer function isAcL = A / (1 + Aβ)

• If the characteristic equation (1 + Aβ)=0, circuit will become unstable, (i.e.) it leads to sustained oscillation

• Re-writing the characteristic equation as(1 –(-Aβ))=0 leads to –Aβ=1

• Magnitude and Phase condition becomes|Aβ|=1 and

• At low frequencies, the resistor in the feedback has no effect, except producing 180 deg. Phase shift.

• However, at high frequencies, for each corner frequencies , an additional phase shift of maximum -90o can take place in open loop gain A.

• For two corner frequencies, it will be -180 deg.• For a specific value of β, Aβ = 1, when A is -180 deg.• This results in oscillation and this instability means

unbounded output.• (1 + Aβ) < 1 (or) Aβ < 0 & AcL > A