E212 – Analog Electronic II Chapter 3 Feedback Amplifier

1.0 Classification of Amplifiers Before proceeding with the concept of feedback it is useful to classify amplifiers into 4 basic categories based on their input & output signal relationships. Voltage amplifier Current amplifier Transconductance amplifier Transresistance amplifier

1.1 Voltage amplifier if then hence with and if then represent the open circuit voltage gain.

1.2 Current amplifier if then hence with and if then represent the short circuit current gain.

1.3 Transconductance amplifier then and if then hence with represent the short circuit mutual or transfer conductance

1.4 Transresistance amplifier then and if then hence with represent the open circuit mutual or transfer resistance.

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

2.1 Positive Feedback Positive feedback is the process when the output is added to the input, amplified again, and this process continues. Example. In a PA system, you get feedback when you put the microphone in front of a speaker and the sound gets uncontrollably loud (you have probably heard this unpleasant effect.

2.2 Negative Feedback Negative feedback is when the output is subtracted from the input. Example. Speed control. If the car starts to speed up above the desired set-point speed, negative feedback causes the throttle to close, thereby reducing speed; similarly, if the car slows, negative feedback acts to open the throttle. The use of negative feedback reduces the gain. Part of the output signal is taken back to the input with a negative sign.

Basic structure of a single - loop feedback amplifier 3.0 Feedback Concept Basic structure of a single - loop feedback amplifier

3.1 Feedback Network This block is usually a passive two-port network. contain resistors, capacitors, and inductors. Usually it is simply a resistive network.

3.2 Sampling Network The output voltage is sampled by connecting the feedback network in shunt across the output. Type of connection is referred to as voltage or shunt or node sampling.

3.2 Sampling Network The output current is sampled by connecting the feedback network in series with the output Type of connection is referred to as current or series or loop sampling.

3.3 Comparator or Mixer Network voltage - applied feedback identified as voltage or series or loop mixing.

3.3 Comparator or Mixer Network current - applied feedback identified as current or shunt or node mixing.

4.0 Feedback Amplifier Topologies Series - shunt shunt - series series - series shunt - shunt

5.0 Feedback Connection Types There are four basic ways of connecting the feedback signal: Voltage-series feedback Voltage-shunt feedback Current-series feedback Current-shunt feedback

Series refers to connecting the feedback signal in series with the input signal voltage. Shunt refers to connecting the feedback signal in shunt (parallel) with an input current source. Fig. 3-2: Feedback amplifier types: (a) voltage-series feedback; (b) voltage-shunt feedback; (c) current-series feedback; (d) current-shunt feedback.

Series feedback connections tend to increase the input resistance, whereas shunt feedback connections tend to decrease the input resistance. Voltage feedback tends to decrease the output impedance, whereas current feedback tends to increase the output impedance.

Gain with Feedback TABLE 3-1: Summary of Gain, Feedback, and Gain with Feedback from Figure 3-2 Voltage-Series Voltage-Shunt Current-Series Current-Shunt Gain without feedback A Feedback β Gain with feedback Af

Voltage-Series Feedback Figure 3-2 (a) below shows the voltage-series feedback connection with a part of the output voltage fed back in series with the input signal. If there is no feedback (Vf = 0), the voltage gain of the amplifier is If a feedback signal Vf is connected with the input in series, the overall voltage gain is (3-1)

Voltage-Shunt Feedback The gain with feedback for the network of Fig. 3-2 (b) is (3-2)

Input Impedance with Feedback Voltage-Series Feedback The input impedance can be determined as follows: (3-3) Fig. 3-3: A more detailed voltage-series feedback connection

Voltage-Shunt Feedback The input impedance can be determined to be: (3-4) Fig. 3-4: A more detailed voltage-shunt feedback connection

Output Impedance with Feedback The output impedance for the connections of Fig. 3-2 is dependent on whether voltage or current feedback is used. For voltage feedback, the output impedance is decreased, whereas current feedback increases the output impedance. Voltage-Series Feedback Referring to Fig. 3-3, the output impedance can be determined by applying a voltage V, resulting in a current I. Then the output resistance with feedback is (3-5)

Current-Series Feedback The output impedance is determined as (3-6) Fig. 3-5: A more detailed current-series feedback connection

A summary of the effect of feedback on input and output impedance is provided in Table 3-2: Voltage-Series Current-Series Voltage-Shunt Current-Shunt Zif (increased) (decreased) Zof

6.0 Negative Feedback Gain The gain with feedback (or closed-loop gain) Af as follows: The quantity A is called the loop gain, and the quantity (1+A) is called the amount of feedback.

6.0 Advantages of Negative Feedback Stabilization of gain make the gain less sensitive to changes in circuit components e.g. due to changes in temperature. Reduce non-linear distortion make the output proportional to the input, keeping the gain constant, independent of signal level. Reduce the effect of noise minimize the contribution to the output of unwanted signals generated in circuit components or extraneous interference.

6.0 Advantages of Negative Feedback 4. Extend the bandwidth of the amplifier Reduce the gain and increase the bandwidth 5. Modification the input and output impedances raise or lower the input and output impedances by selection of the appropriate feedback topology.

6.1 Stabilization of Gain Stabilization of the gain of an amplifier against changes in the components (e.g., with temperature, frequency) If you represent the gain without feedback (the open loop gain) by Ao, then the system gain with negative feedback is where  is the fraction of the output which feeds back as a negative voltage at the input. The extent of this stabilizing influence can be illustrated as follows:

6.1 Stabilization of Gain

6.2 Decreasing Distortion/noise with Feedback The use of negative feedback can discriminate against sources of noise or distortion within an amplifier.

6.2 Decreasing Distortion/noise with Feedback showing that distortion within the feedback loop is discriminated against, with more reduction of distortion which arises near the output.

6.3 Increasing the Bandwidth

6.4 Modification of input and output impedance i) Input Resistance The input resistance with negative feedback will be raised for series or voltage mixing.

6.4 Modification of input and output impedance i) Input Resistance The input resistance with negative feedback will be lowered for shunt or current mixing.

6.4 Modification of input and output impedance ii) Output Resistance The output resistance with negative feedback will be lowered for shunt or voltage sampling. Let replaced load with test voltage

6.4 Modification of input and output impedance ii) Output Resistance The output resistance with negative feedback will be raised for series or current sampling. The output resistance with feedback for current or series sampling to be:

6.4 Modification of input and output impedance Summary For a series connection at input or output, the resistance is increased by (1+A) and For a shunt connection at input or output, the resistance is lowered by (1+A).

7.0 Practical Feedback Circuits Voltage-Series Feedback The feedback voltage Vf is connected in series with the source signal Vs, their difference being the input signal Vi. Without feedback the amplifier gain is (3-7) where, gm = transconductance factor Fig. 3-7: FET amplifier with voltage-series feedback.

Whereas RL is combination of resistors: The feedback network provides a feedback factor of Using the values of A and β, we find the gain with negative feedback to be If βA >>1, we have (3-7)

Current-Series Feedback Fig. 3-8: (a) a single transistor amplifier circuit and (b) ac equivalent circuit without feedback The feedback voltage VE is resulted in by the current through resistor RE.

The input and output impedances are, respectively, Without Feedback Referring to the Fig. 3-8 and summarized in Table 3-1, we have (3-8) (3-9) The input and output impedances are, respectively, (3-10) (3-11)

With Feedback (3-12) The input and output impedances are calculated as specified in Table 3-2, (3-13) (3-14)

The voltage gain A with feedback is (3-15)

Voltage-Shunt Feedback Fig. 3-9: Voltage-shunt negative feedback amplifier: (a) constant-gain circuit; (b) equivalent circuit. Referring to Fig. 3-9 and Table 3-1 and the op-amp ideal characteristics Ii = 0, Vi = 0, and voltage gain of infinity, for a constant-gain we have: (3-16) (3-17)

The gain with feedback is then (3-18) The more usual gain is the voltage gain with feedback, (3-19)

Fig. 3-10: Voltage-shunt feedback amplifier using an FET: (a) circuit; (b) equivalent circuit.

With feedback, the gain of the circuit is, With no feedback, Vf = 0, (3-20) The feedback is, (3-21) With feedback, the gain of the circuit is, (3-22)

The voltage gain of the circuit with feedback is then Or, (3-23) The voltage gain of the circuit with feedback is then (3-24)