EC16403 ELECTRONIC CIRCUITS II

UNIT I FEEDBACK AMPLIFIERS

Topics to be covered Introduction to basic amplifiers and equivalent circuits, General Feedback Structure Properties of negative feedback Basic Feedback Topologies Feedback amplifiers – Series – Shunt, Series – Series, Shunt – Shunt and Shunt – Series Feedback Comparison of four feedback topologies. Determining the Loop Gain, Stability Problem– Nyquist Plot Effect of feedback on amplifier poles Frequency Compensation.

Amplifier Amplifiers are the properly biased transistor circuit which are used to amplify input signal (either ac current or voltage) to output signal (ac current or voltage).

Introduction to Feedback Feedback is used in virtually all amplifier system In feedback system, a signal that is proportional to the output is fed back to the input and combined with the input signal to produce a desired system response. However, unintentional and undesired system response may be produced.

Feedback Amplifier Feedback is a technique where a proportion of the output of a system (amplifier) is fed back and recombined with input There are 2 types of feedback amplifier: Positive feedback Negative feedback

Negative Feedback Negative feedback is when the output is subtracted from the input. The use of negative feedback reduces the gain. Part of the output signal is taken back to the input with a negative sign.

Properties of negative feedback amplifier Gain reduction. Bandwidth extension. Multiple poles. Replacement of the feedback network with a two-port. Small-signal circuit. Loaded open-loop gain. Gain with feedback. Input and output resistances.

Negative feedback takes a sample of the output signal and applies it to the input to get several desirable properties. In amplifiers, negative feedback can be applied to get the following properties – Desensitized gain – gain less sensitive to circuit component variations – Reduce nonlinear distortion – output proportional to input (constant gain independent of signal level) – Reduce effect of noise – Control input and output impedances – by applying appropriate feedback topologies – Extend bandwidth of amplifier All of these properties can be achieved by trading off gain

Assume that  is constant. Gain Desensitivity Assume that  is constant. A  xo  A f xs 1  A dAf  1 dA (1  A )2 dA dA  f (1  A )2 dA f  1 dA Af (1  A ) A The percentage change in Af (due to variations in some circuit parameter) is smaller than the percentage change in A by amount of feedback. The amount of feedback, 1 + A, is also known as the desensitivity factor.

 : the upper 3-dB frequency Bandwidth Extension Consider an amplifier whose high-frequency response is characterized by a single pole. AM A(s) = AM : the midband gain 1 + s  : the upper 3-dB frequency H Apply the negative feedback with a frequency-independent factor  : AM A(s) 1  AM  Close - loop gain A (s)  = f 1  A(s) 1  s H (1  AM  )

Negative feedback is applied to improve SNR: Noise Reduction Vs : input signal Vo : output signal Vn : noise or interference A1 : gain Singal - to - noise ratio S = Vs N Vn The amplifier suffers from noise and the noise can be assumed to be introduced at the input of the amplifier. Negative feedback is applied to improve SNR:  A1A2 A1 V  V  V o s n (clean amp.) 1  A1A2 1  A1A2  S  Vs N V A2

Reduction in Nonlinear Distortion Curve (a) shows the amplifier transfer characteristic without feedback. Curve (b) shows the characteristic with negative feedback (β = 0.01) applied. The open-loop voltage transfer characteristic of the amplifier is change from 1000 to 100 and then to 0. [curve (a)] Apply negative feedback with β = 0.01 to the amplifier [curve (b)] : the slope of the steepest segment: the slope of the next segment: The order-of-magnitude change in slop is considerably reduced. The price paid is a reduction in voltage gain.

Based on the quantity to be amplified (voltage or current) and on the desired form of the output (voltage or current), amplifiers can be classified into four categories. Voltage amplifiers Current amplifiers Transconductance amplifiers Transresistance amplifiers Four basic feedback topologies: Voltage-sampling series-mixing (series-shunt) topology Current-sampling shunt-mixing (shunt-series) topology Current-sampling series-mixing (series-series) topology Voltage-sampling shunt-mixing (shunt-shunt) topology

Basic Feedback Topologies

Voltage Amplifiers Characteristics: Input signal: voltage output signal: voltage Voltage-controlled voltage source High input impedance Low output impedance Feedback topology Voltage-sampling series-mixing (series-shunt) topology The feedback network samples the output voltage, and the feedback signal xf is a voltage that can be mixed with the source voltage in series. “Series” refers to the connection at the input and “shunt” refers to the connection at the output. Stabilize the voltage gain Higher input resistance(series connection at the input) Lower output resistance(parallel connection at the output)

Voltage-sampling series-mixing (series shunt topology) Example:

Current Amplifiers Characteristics: Input signal: current output signal: current Current-controlled current source Low input impedance High output impedance Feedback topology Current-sampling shunt-mixing (shunt-series) topology The feedback network samples the output current, and the feedback signal xf is a current that can be mixed in shunt with the source current. “Shunt” refers to the connection at the input and “series” refers to the connection at the output. Stabilize the current gain Lower input resistance (shunt connection at the input) Higher output resistance (series connection at the output)

Current-sampling shunt-mixing (Shunt series topology) Example:

Transconductance Amplifiers Characteristics: Input signal: voltage output signal: current Voltage-controlled current source High input impedance High output impedance Feedback topology Current-sampling series-mixing (series-series) topology The feedback network samples the output current, and the feedback signal xf is a voltage that can be mixed with the source voltage in series. “Series” refers to the connection at the input and “series” refers to the connection at the output. Stabilize the transconductance gain Higher input resistance (series connection at the input) Higher output resistance (series connection at the output)

Current-sampling series-mixing (Series series topology) Example:

Transresistance Amplifiers Characteristics: Input signal: current output signal: voltage Current-controlled voltage source Low input impedance Low output impedance Feedback topology Voltage-sampling shunt-mixing (shunt-shunt) topology The feedback network samples the output voltage, and the feedback signal xf is a current that can be mixed in with shunt the source current. “Shunt” refers to the connection at the input and “shunt” refers to the connection at the output. Stabilize the transresistance gain Lower input resistance (shunt connection at the input) Lower output resistance (shunt connection at the output)

Voltage-sampling shunt-mixing (Shunt shunt topology) Example:

A circuit: a unilateral open-loop amplifier The Series-Shunt Feedback Amplifier A circuit: a unilateral open-loop amplifier Ri : input resistance Ro : output resistance  circuit: an ideal voltage-sampling series-mixing feedback network The source and load resistances are included inside the A circuit. The  circuit does not load the A circuit. Ö Do not change A  Vo /Vi.

Equivalent circuit The close-loop gain (A and  have reciprocal units) o Input resistance Ö The series-mixing increases the input resistance by (1 + A). General form Zif (s) = Zif (s)[1 + A(s)(s)]

Output resistance (Vs = 0)

Summary of the Series-Shunt Feedback Amplifier

Series-Series Feedback Amplifier The Ideal Situation of the Series-Series Feedback Amplifier Ideal structure A circuit: a unilateral open-loop amplifier Ri : input resistance Ro : output resistance  circuit: an ideal current-sampling series-mixing feedback network The source and load resistances are included inside the A circuit. The  circuit does not load the A circuit. Ö Do not change A  Io /Vi.

(A and  have reciprocal units) Equivalent circuit The close-loop gain (A and  have reciprocal units) o Input resistance The series-mixing increases the input resistance by (1 + A ). General form Zif (s) = Zi (s)[1 + A(s)(s)]

Output resistance (Vs = 0) of t Output resistance  V R of I t In this case, Vi  V f  Io  It (for Vs  0) Ö V  (It  AVi )Ro  (It  AIt )Ro The voltage-sampling feedback increases the output resistance by (1 + A ). General form Zof (s)  Zo (s)[1  A(s) (s)]

Summary of the Series-Series Feedback Amplifier

The Shunt-Shunt Feedback Amplifier The Ideal Situation of the Shunt-Shunt Feedback Amplifier Ideal structure A circuit: a unilateral open-loop amplifier Ri : input resistance Ro : output resistance  circuit (transconductance): an ideal voltage-sampling shunt-mixing feedback network The source and load resistances are included inside the A circuit. The  circuit does not load the A circuit. Ö Do not change A  Vo /Ii.

Equivalent circuit The close-loop gain (A and  have reciprocal units) o Input resistance Ö The shunt-mixing reduces the input resistance by (1 + A ). General form

Output resistance (Vs = 0) where and The voltage-sampling feedback reduces the output resistance by (1 + A).

Summary of the Shunt-Shunt Feedback Amplifier

The Shunt-Series Feedback Amplifier The Ideal Situation of the Shunt-Series Feedback Amplifier Ideal structure A circuit: a unilateral open-loop amplifier Ri : input resistance Ro : output resistance  circuit : an ideal current-sampling shunt-mixing feedback network The source and load resistances are included inside the A circuit. The  circuit does not load the A circuit. Ö Do not change A  Io /Ii.

Equivalent circuit The close-loop gain (A and  have reciprocal units) o Input resistance Ö The series-mixing reduces the input resistance by (1 + A ). General form

Output resistance (Vs = 0) In this case, Ii  I f  Io  It (for Is = 0) Ö V  (It  AIi )Ro  (It  AIt )Ro The current-sampling feedback increases the output resistance by (1 + A ). General form Zof (s)  Zo (s)[1  A(s) (s)]

Summary of the Shunt-Series Feedback Amplifier

Summary of Relationships for the Four Feedback_Amplifier Topologies

Determining the Loop Gain Loop gain A is a very important quantity that characterizes a feedback loop. Find the loop gain: Let the external source xs = 0 . Open the feedback loop by breaking the connection of xo to the feedback network and apply a test signal xt . Determine the loop gain: xf = xt Ö xi = xf = xt Ö xo = Axi = Axt Loop gain A = xo /xt The loop gain A is given by the negative of the ratio of the returned signal to the applied test signal.

The loop gain A = Vr /Vt , where Vr is the returned voltage. A conceptual feedback loop is broken at XX’ and a test voltage xt is applied. The impedance Zt is equal to that previously seen looking to the left of XX’. The loop gain A = Vr /Vt , where Vr is the returned voltage. A  Vr Vt As an alternative, A can be determined by finding the open-circuit transfer function Toc and the short-circuit transfer function Tsc and combining them as indicated. open-circuit transfer function Toc short-circuit transfer function Tsc

Closed-loop circuit: Break XX’ to determine the loop gain A

Break YY’ to determine Toc and Tsc : Open-circuit transfer function Toc Short-circuit transfer function Tsc

Equivalence of Circuits from a Feedback-Loop Point of View Break XX’ to determine the loop gain A :

The Stability Problem Stability Problem of a Feedback Amplifier The closed-loop transfer function of a feedback amplifier where A(s) : the open-loop transfer function  (s) : the feedback transfer function For physical frequencies s = j , If for s = j0, L(j0) = 1, then the closed-loop gain approaches infinity at 0. Under this condition, the circuit amplifies its own noise components at 0 indefinely. Barkhausen criteria: If a negative-feedback circuit has a loop gain that satisfies two conditions:L(j0)  1 and L(j0) = 180o, then the circuit may oscillate at 0. In order to ensure oscillation in the presence of temperature and process variations, we typically choose the loop gain to be at least twice or three times the required value. Oscillations could occur in a negative-feedback amplifier, we wish to find methods to prevent their occurrence.

Nyquist Plot Nyquist criterion: If the intersection occurs to the left of (-1, 0), the magnitude of loop gain at this frequency is greater than unity and the amplifier will be unstable. If the intersection occurs to the right of (-1, 0), the amplifier will be stable.

Effect Of Feedback On The Amplifier Poles Stability and Pole Location Consider an amplifier with a pole pair at s = 0  jn . v(t) = e 0t [e +jnt + e jnt ] = 2 e 0t cos (nt ) Relationship between pole location and transient response: The existence of any right-half-plane poles results in instability.

Poles of the Feedback Amplifier The closed-loop transfer function of a feedback amplifier where A(s) : the open-loop transfer function  (s) : the feedback transfer function Find poles: The poles of the feedback amplifier are the zeros of 1 + A(s) (s). 1 + A(s) (s) = 0 (the characteristic equation of the feedback loop.) It should therefore be apparent that applying feedback to an amplifier changes its poles.

Frequency Compensation Theory of Frequency Compensation A A’ :Introduce an additional pole at fD . poles: fD, fP1, fP2, fP3, …. A” :Move the original low- frequency pole to f ’D . (i.e., fP1  f ’D ) poles: f ’D, fP2, fP3, …  = 102

Implementation of Frequency Compensation Two-Cascaded gain stages of a multistage amplifier Equivalent circuit for the interface The circuit with a compensating between the two stages capacitor CC added