Advanced Circuit Techniques In Class Work
The op-amp in the circuit below is non-ideal and has the following parameters: 𝑅𝑖 = 25K, 𝑅𝑜 = 200 Ω,
and the gain is . Further, 𝑅𝐼 = 1K, 𝑅𝐿 = 2K, 𝑅2 = 91K, and 𝑅1 = 10K.
𝑣1 = ℎ11 𝑖1 + ℎ12 𝑣2
𝑖2 = ℎ21 𝑖1 + ℎ22 𝑣2
(a) Feedback Amplifier
(b) h-parameters
Using two-port theory, determine the gain 𝐴𝑓 = 𝑣𝑜 ⁄𝑣𝑖 , and the input- and output resistances 𝑅𝑖𝑓 and 𝑅𝑜𝑓
of the feedback amplifier. Determine the input- and output resistances of the amplifier proper, namely
𝑅𝑖𝑥 and 𝑅𝑜𝑥 . Use h-parameters to model the feedback network. It is important that you show your work.
For example, show how you calculate the h-parameters, redraw the circuits with the amplifier and the
feedback network replaced with two-ports, etc. Show that ℎ11 = 9.01K, ℎ22 = 1⁄101K and ℎ12 =
1⁄10.1. You may assume no feed forward for the feedback network. (25 points)
Solution
The figure below summarizes the calculations for the h-parameters for the feedback network. Since there
is no feed forward, ℎ21 = 0.
ℎ11 =
𝑣1
= 𝑅1 ‖𝑅2 = 9.01K
𝑖1
ℎ22 =
𝑖2
1
1
=
=
𝑣2
𝑅1 + 𝑅2 101K
ℎ12 =
𝑣1
𝑅1
1
=
=
𝑣2
𝑅1 + 𝑅2 10.1
Below is the two-port equivalent of the amplifier. Since there is no feed forward, ℎ21 = 0, and the
controlled current source associated with this parameter was removed from the circuit.
1
Next, turn off the feedback by setting ℎ12 = 0, which is the same as shorting the voltage source. The gain
of the resulting amplifier is
𝐴=
25K
1.961K
(104 )
= 4,729
1K + 25K + 9.01K
1.961K + 1K
The improvement factor is (1 + 𝛽𝐴) = (1 + ℎ12 𝐴) = 469. The closed-loop gain is
𝐴𝑓 =
𝐴
4,729
=
= 10.1
1 + 𝛽𝐴
469
The closed-loop input resistance is 𝑅𝑖𝑓 = (1 + 𝛽𝐴)(1K + 25K + 9.01K) = 16.4M.
The closed-loop output resistance is
𝑅𝑜𝑓 =
2K‖101K‖1K
= 1.41 Ω
469
Finally 𝑅𝑖𝑥 = 16.4M − 1K ≈ 16.4M and
1
1
1
=
−
⇒ 𝑅𝑜𝑥 ≈ 1.41 Ω
𝑅𝑜𝑥 𝑅𝑜𝑓 2K
2