Closed-Loop Response – Op-amps are normally used in a closed loop configuration with negative feedback. – This achieves precise control over the gai

Closed-Loop Response

– Op-amps are normally used in a closed loop configuration with negative feedback.

– This achieves precise control over the gain and bandwidth of the circuit..

– Remember that in an inverting or noninverting configuration, we define

B = R_i/( R_i + R_f)

– The closed loop critical frequency of an op-amp is:

f_cu(cl) = f_cu(ol)(1 + BA_ol(mid))

– Thus, the closed-loop critical frequency, f_cu(cl), is higher than the open-loop critical frequency, f_cu(ol)^.

– The bandwidth is, thus, increased by the same factor:

BW_cl = BW_ol(1 + BA_ol(mid))

– The product between the gain and the bandwidth is always constant.

– This is true as long as the roll-off is fixed.

– Then:

A_clf_cu(cl) = A_olf_cu(ol)

– The gain-bandwidth product is always equal to the frequency at which the op-amp’s open-loop gain is unity (0 dB), or unity-gain bandwidth.

Unity-gain bandwidth = A_clf_cl(cl)

Example

Determine the bandwidth of each of the amplifiers shown below. Both op-amps have an open-loop gain of 100 dB and a unity-gain bandwidth if 3 MHz.

Solution

a) For the noninverting amplifier of (a), the closed loop gain is:

A_cl @ 1/B = 1 + R_f/R_i = 1+220k?/3.3k? = 67.7

We know the closed loop critical frequency equals the bandwidth, thus

f_c(cl) = BW_cl =(unity-gain BW)/A_cl

BW_cl = 3 MHz/67.7 = 44.3 kHz

b) For the inverting amplifier in (b), the closed loop gain is:

A_cl = - R_f/R_i =-47k?/1.0k? = -47

Using the absolute value of A_cl, the closed loop bandwidth is:

BW_cl = 3 MHz/47 = 63.8 kHz