Please show steps Determine the dosed-loop gain in/Vsig of the transconductance
ID: 1846411 • Letter: P
Question
Please show steps
Determine the dosed-loop gain in/Vsig of the transconductance amplifier (voltage-controlled current source) below. Assume that the operational amplifier has an open-loop gain Avg of 10,000 V/V, differential-input resistance Rd = 5K, open-loop output resistance Ro = 100ohm. Redraw the system with the feedback network Rs, Rf, and Rin) replaced by a two-port network represented by z-parameters. Combine Rsig, RL, and two-port parameters Z11 and Z22 with the op amp model to determine the forward gain A; calculate two-port parameter Z12 to determine beta . Then determine the closed-loop gain. Explain why the effect of Z21 may be ignored.Explanation / Answer
a.
fro the first part we will assmume it to be a ideal op-AMP.
so no input current is going into the positive or negative terminal. also the volatge at bothe the ports are equal.
the current is branching between two branches. the part of the current flowing through the Rin and RF
Iin = Io*(10/20000 + 10) A-----------------------------------------1).
again as the negative port will will hold Vin voltage so,
Iin = Vin/Rin A--------------------------------2)
solving equation 1 and 2 we get
Gm = Io/Vin = 1.0005 A/V
b. as open loop gain is 10,000 then we can use the same ogic as done above.
as u hae seen the current is branching between 20k and 10 ohm. so net resistance seen from the output can be approxmated as
Rl = 250 + 10 ohm =260 ohm.
now we can write
Vin/2000 = il-------------------------1
and
(Vo/260)*(10/20010) =il-------------2
equating we get
Vo/Vin = 260 (approximately)
to calculate beta, we know that this is the part of the output fed back to the input. or this is the voltage appear at the negativ eterminalof the opamp.
so, beta = 10/260 *(2/20) = 1/260 approximately.
u can also check it as close loop gain =(1/beta) when open loop gain is very high.