Closed Loop Responce
– 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 = Ri/( Ri + Rf)
– The closed loop critical frequency of an op-amp is:
fcu(cl) = fcu(ol)(1 + BAol(mid))
– Thus, the closed-loop critical frequency, fcu(cl), is higher than the open-loop critical frequency, fcu(ol).
– The bandwidth is, thus, increased by the same factor:
BWcl = BWol(1 + BAol(mid))
– The product between the gain and the bandwidth is always constant.
– This is true as long as the roll-off is fixed.
Aclfcu(cl) = Aolfcu(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 = Aclfcl(cl)
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.
a) For the noninverting amplifier of (a), the closed loop gain is:
Acl @ 1/B = 1 + Rf/Ri = 1+220k?/3.3k? = 67.7
We know the closed loop critical frequency equals the bandwidth, thus
fc(cl) = BWcl =(unity-gain BW)/Acl
BWcl = 3 MHz/67.7 = 44.3 kHz
b) For the inverting amplifier in (b), the closed loop gain is:
Acl = - Rf/Ri =-47k?/1.0k? = -47
Using the absolute value of Acl, the closed loop bandwidth is:
BWcl = 3 MHz/47 = 63.8 kHz