E3 238 Analog VLSI Circuits
Lecture 19: Feedback
Gaurab Banerjee
Department of Electrical Communication Engineering,
Indian Institute of Science, Bangalore
banerjee@ece.iisc.ernet.in
Generalized Feedback Network
Virtual Ground
( = A)
Key Components:
•
Feed-forward Amplifier
•
Sense Mechanism
(Output)
•
Feedback Network
•
Return Mechanism (Input)
-> Input of H(s) = virtual ground -> signal amplitude is very small
-> G(s) = β (usually frequency independent) -> β A = loop gain
Closed loop
transfer
function
Properties of Feedback
-> Gain Desensitization:
-> Closed loop gain determined by the feedback factor, for large A
-> Large variations in A translate into small variations in Y/X -> gain
desensitization
-> Tradeoff between precision and closed loop gain
Properties of Feedback
-> Bandwidth Modification:
Consider a single pole transfer function:
Numerator = closed loop gain at low frequencies
Denominator = Pole at (1+ β A0) ω0 -> 3 dB bandwidth increases by (1+ β A0)
Properties of Feedback
-> Terminal Impedance Modification:
Output impedance when output voltage is measured in shunt and proportional
voltage is applied in series:
Voltage measured in “shunt” -> This type of feedback lowers impedance
Properties of Feedback
-> Input Impedance for the same configuration:
Voltage applied at the input in “series” -> This type of feedback increases
impedance
Sense and Return Mechanisms
SENSING:
Voltage sensed in shunt ->
“shunt feedback”
Current sensed in series ->
“series feedback”
RETURN MECHANISM:
Voltage addition -> “series”
Current addition -> “shunt”
Nomenclature of Feedback Type
First Term (return or input applied) - Second Term (sense or output)
Shunt-Series: Current Sensed, Current Applied
Shunt-Shunt: Voltage Sensed, Current Applied
Series-Shunt: Voltage Sensed, Voltage Applied
Series-Series: Current Sensed, Voltage Applied
Terminal Impedance Modification
Consider the circuit for which we looked at terminal impedance modification
-> voltage is measured: shunt, voltage is returned: series
Series-Shunt feedback
Type of feedback
Input Impedance Multiplier
Output Impedance
Multiplier
Qualitative Understanding
At outputs:
Series feedback measures current -> Regulates current
-> “like a constant current source -> High Z
Shunt feedback measures voltage -> Regulates voltage
-> “like a constant voltage source” -> low Z
At inputs:
Series feedback applies voltage to minimize current error*
-> makes current constant -> High Z
Shunt feedback applies current to minimize voltage error*
-> makes voltage constant -> Low Z
*This is more of a “memory aid”. Actual voltage/current return at input
is topology specific.
An Example: Series-Series Feedback
Current measured in
series -> Applied at the
input in series, as a
voltage
•
This is sometimes known as “emitter feedback” or “local series feedback”
•
Note that an emitter follower, which looks similar, has its output voltage sampled
and returned as a voltage: so, emitter follower has series-shunt feedback
Calculation of Loop Gain
-> Set the main input to zero
-> Break the loop at some point
-> Inject a test signal in the direction of feedback
-> Follow the signal, obtain the signal that returns to the break point
negative of the transfer function thus derived = loop gain
In the figure above:
First order analysis neglects:
a) loading effects due to feedback network
b) non-unilateral feedback
Circuit Example
Assume that Vx is externally biased
with no impact on circuit ->
KCL at node Vx:
KCL at node Vout:
Note that the transfer function has a RHP zero (high frequency) and a pole.
At low frequencies:
Circuit Example
Now, consider feedback ->
-> Feedback based analysis provides a good approximation
-> Note that this analysis does not predict the feed-forward zero.
Loading Effects
Loading
-> In an ideal system, we neglect the impact of the feedback network loading
the open loop circuit.
-> In real circuits, this may not always be negligible
-> Solution: Model the feedback network in terms of Z,Y, H or G parameters
and calculate the impact of loading
-> Not as simple as it sounds! Sometimes, it is better to get qualitative
understanding from “unloaded” feedback analysis and refine the final results
with KCL/KVL or circuit simulations.