EFB2053: Microelectronic Circuits - JAN 2024 Feedback and Stability Lecturer: Phone: Office: E-mail: Dr Saiful Azrin bin Mohd Zulkifli 05-368 7852 / 019-571 8675 Room 23-03-12 saifulazrin_mz@utp.edu.my Slides prepared by: AP Dr. Mohd Haris Md Khir Feedback & Stability In this chapter, we will: • Obtain the transfer function of the ideal feedback system. • Analyze the four ideal feedback circuit configurations. • – series–shunt feedback amplifiers. – shunt–series feedback amplifiers. – series-series feedback amplifiers. – shunt–shunt feedback amplifiers. Derive the loop-gain of ideal and practical feedback circuits and determine the stability criteria of feedback circuits. 2 Feedback & Stability Introduction • Feedback can be either negative or positive. • For negative feedback, a portion of output signal is subtracted from the input signal. • For positive feedback, a portion of the output signal is added to the input signal. • Positive feedback is used in the design of oscillators. • Advantages of Negative Feedback System: - Gain sensitivity: Variations in amplifier gain as a result of changes in transistor parameters are reduced by feedback. Bandwidth extension: The bandwidth that uses negative fb is larger than of the basic amplifier. Noise sensitivity: Increase the signal-to-noise ration with fb system. Reduction of nonlinear distortion: Negative feedback reduces distortion that may appear in the output signals. Control of impedance levels: Input & output impedances can be increased or decreased with fb. 3 Feedback & Stability • Disadvantages of Negative Feedback System: - Circuit gain: The overall amplifier gain with feedback is reduced. Stability: There is a possibility that feedback circuit may become unstable at high frequencies. 4 Feedback & Stability Basic Feedback Concepts • Figure shows the basic configuration of a feedback amplifier. • S can be either currents or voltages. A is the open-loop gain. Sfb is a feedback signal. • The feedback signal is subtracted from the input signal and producing the error signal, SE. • The subtraction property produces the negative feedback. 5 Feedback & Stability • From the figure, πΊπΆ = π¨πΊπ A= Amplification factor πΊππ = π·πΊπΆ β= feedback transfer function Normally, the error signal is small and βA >> 1, therefore At the summing junction, πΊπΊ = πΊπ − πΊππ Combining the equations, π¨π ≅ πΊπΆ = π¨ πΊπ − π·πΊπΆ = π¨πΊπ − π·π¨πΊπΆ The closed-loop transfer function is therefore given by, π¨π = πΊπΆ π¨ = πΊπ π+π·π¨ or π¨ π = π·π¨ π· Feedback amplifier is a function of the feedback network only. π¨ π¨π = π+π» T = loop gain 6 Feedback & Stability If assuming a large loop gain, then the output signal becomes π¨ π πΊπΆ = πΊ ≅ .πΊ π + π·π¨ π π· π π¨π = πΊπΆ π¨ = πΊπ π+π·π¨ After substitution, the error signal is obtained as πΊπ¬ = πΊπ − π·πΊπΆ ≅ πΊπ − π· πΊπ π· =0 With large loop gain, the error signal decreases to almost ZERO. 7 Feedback & Stability Gain Sensitivity • If β is constant, taking the derivative of Af with respect to A, produces π π¨π π π¨ = − π π¨ π + π·π¨ π + π·π¨ π π¨π = π π¨ π + π·π¨ π π . π· = π + π·π¨ π π Divide both sides by the closed-loop gain, yield π π¨ π π¨π π¨π π π¨ π π π¨ π + π·π¨ π = = . = π¨ π¨π π + π·π¨ π¨ π¨ π¨ π + π·π¨ 8 Feedback & Stability 9 Feedback & Stability Bandwidth Extension • The closed-loop gain of the feedback amplifier can be expressed as: π¨π π = π¨ π π¨ π = π + π·π¨ π π¨πΆ . π + π·π¨πΆ π + π π+π π― Single pole TF Substitute the right equation, π¨π π = π¨πΆ π ππ― π π + π·π¨πΆ From above equation, it’s noted that the lowfreq. closed-loop gain is smaller than the open-loop gain by the factor of (1+βAo) BUT the closed-loop 3 dB-freq. is larger than the open-loop, also by the same factor. 10 Feedback & Stability 11 Feedback & Stability Noise Sensitivity • Unwanted or random noise may present in the signal. • Negative feedback may reduce the noise level and increase the SNR. The input signal-to-noise ratio is defined as, πΊπ΅πΉ π πΊπ ππ = = π΅π ππ The output signal-to-noise ratio is defined as, πΊπ΅πΉ π = πΊπ π¨π»π πΊπ = π΅π π¨π»π π΅π Ati is the amplification factor of the source signal Atn is the amplification factor of the noise signal 12 Feedback & Stability Example Determine the effect of feedback on the source signal and noise signal for the system below. For system (a): πππ¨ = π¨π π¨π ππ + π¨π ππ πΊπΆ πππππ πΊπ = = ππ π΅πΆ ππππ π΅π For system (b): πππ = π¨π π¨π ππ + π¨π π¨π ππ = πππππ + πππππ πΊπΆ πππππ πΊπ = = π΅πΆ πππππ π΅π 13 Feedback & Stability Example 2 Determine the effect of feedback on the source signal and noise signal for the system below. For system (c): πππͺ = π¨π π¨π ππ¬ + π¨π ππ πππ = π·πππͺ ππ¬ = ππ − πππ = ππ − π·πππͺ Through substitution, πππͺ = π¨π π¨π ππ − π·πππͺ + π¨π ππ or, πππͺ = π¨π π¨π π¨π . ππ + . ππ π + π·π¨π π¨π π + π·π¨π π¨π ≅ πππππ + π. πππ πΊπΆ πππππ πΊπ = = ππππ π΅πΆ π. πππ π΅π Example (3) produces the largest SNR. This configuration may occur when amplifier A2 is an audio power-amplifier stage while A1 is the low-noise preamplifier. 14 Feedback & Stability Ideal Feedback Topologies • There are four basic feedback topologies. • Series-Shunt (voltage amplifier) • Shunt-Series (current amplifier) • Series-Series (transconductance amplifier) • Shunt-Shunt (transresistance amplifier) 15 Feedback & Stability Series-Shunt Configuration (Voltage-Amplifier) • The equivalent circuit for the amplifier as shown below: • The circuit consists of a basic voltage amplifier with input resistance, Ri and an open-loop voltage gain, Av. • The feedback circuit samples output voltage and produces feedback voltage, Vfb. If no-load is connected, then the output voltage is given by, π½πΆ = π¨π π½π¬ And, π½ππ = π·π½πΆ = π·π π½πΆ 16 Feedback & Stability The error voltage, assuming the source resistance, Rs is negligible is given by, π½π¬ = π½π − π½ππ π½πΆ = π¨π π½π¬ π½ππ = π·π π½πΆ Combining the equation yield, π¨ππ = π½πΆ π¨π = π½π π+π·π π¨π Above equation is the closed-loop voltage gain of the feedback amplifier The input resistance, Rif can be determined as follows: π½π = π½π¬ + π½ππ = π½π¬ + π·π π½πΆ = π½π¬ + π·π½ π¨π½ π½π¬ or, π½π¬ = π½π π + π·π½ π¨π 17 Feedback & Stability The input current is given by, π½π¬ π½π π°π = = πΉπ πΉπ π + π·π π¨π The input resistance with feedback is given by, πΉππ = π½π = πΉπ π + π·π π¨π π°π 18 Feedback & Stability The output resistance, Rof can be determined as follows: The input signal voltage source is set equal to zero (short cct), and a test voltage is applied to the terminals. From the circuit, π½π¬ + π½ππ = π½π¬ + π·π π½π = π π½π¬ = −π·π½ π½π The output current is, π½π − π¨π π½π¬ π½π − π¨π −π·π π½π = πΉπ πΉπ π½π πΉπ π½π π + π·π π¨π πΉππ = = π°π = π°π π + π·π π¨π πΉπ π°π = 19 Feedback & Stability 20 Feedback & Stability Shunt-Series Configuration (Current-Amplifier) • The equivalent circuit for the amplifier as shown below: • The circuit consists of a basic current amplifier with input resistance, Ri and an open-loop current gain, Ai. • The feedback circuit samples output current and produces feedback current, Ifb. • Iο₯ is the diff between input signal and the feedback current. • Input source is a Norton equivalent cct. The output & feedback currents are, π°πΆ = π¨π π°π and π°ππ = π·π π°πΆ Rs is normally large therefore, π°π = π°πΊ + π°ππ 21 Feedback & Stability Combining the previous eqns. Produces the closed-loop current gain, π¨ππ = π°πΆ π¨π = π°π π + π·π π¨π To determine the input resistance, Rif, π°π = π°πΊ + π°ππ = π°πΊ + π·π π°π = π°πΊ + π·π π¨π π°πΊ or, π°π π°πΊ = π + π·π π¨π The input resistance is therefore, πΉππ = π½π πΉπ = π°π π + π·π π¨π The input voltage is, π½π =π°πΊ πΉπ = π°π πΉπ π+π·π π¨π 22 Feedback & Stability • The output resistance can be determined using the following equiv. cct. • The input signal is set to zero (open cct for current source) & Test current is applied to the o/p. π°πΊ + π°ππ =π°πΊ + π·π π°π = π or, π°πΊ = −π·π π°π The output voltage is given by, π½π = π°π − π¨π π°πΊ πΉπ = π°π − π¨π −π·π π°π πΉπ = π°π π + π·π π¨π πΉπ πΉππ π½π = = π + π·π π¨π πΉπ π°π 23 Feedback & Stability Finally, the equivalent circuit of this feedback current amplifier is shown below, π°πΆ π¨π = π°π π + π·π π¨π π½π πΉπ πΉππ = = π°π π + π·π π¨π π½π πΉππ = = π + π·π π¨π πΉπ π°π π¨ππ = 24 Feedback & Stability π°πΆ π¨π = π°π π + π·π π¨π π½π πΉπ πΉππ = = π°π π + π·π π¨π π½π πΉππ = = π + π·π π¨π πΉπ π°π π¨ππ = 25 Feedback & Stability Op-Amp Series-Shunt Feedback Circuit • Analyzing an op-amp of the series-shunt feedback configuration. • Av = Amplifier voltage gain and βv = voltage feedback transfer function. • In ideal feedback cct., Av is normally very large, π¨ππ = π¨ππ π¨π π + π·π π¨π π½π π = ≅ π½π π·π 26 Feedback & Stability • The equivalent cct. Is shown below. • From previous analysis on the ideal non-inverting amplifier in Chapter 9, we found that: π¨ππ = π¨ππ π½π π = ≅ π½π π·π π½π πΉπ = π+ π½π πΉπ Inserting the known eqn, the feedback transfer function, βv is therefore given by, π·π = π πΉ π + πΉπ π 27 Feedback & Stability Ro is normally small, Ro ο» 0, therefore, π½π = π¨π π½πΊ π½πΊ = π½π − π½ππ Through substitution, π½π = π¨π π½π − π½ππ Assuming the input resistance, Ri is very large, the feedback voltage is therefore given by π½ππ ≅ πΉπ π½ πΉπ + πΉπ π Finally, π¨ππ π½π π¨π = = π¨π π½π π + πΉ π + πΉπ π π¨ππ = π¨π π + π·π π¨π 28 Feedback & Stability To determine Rif, π½π = π½πΊ + πΉπ π¨π π½πΊ π½π = π½πΊ + πΉ πΉπ + πΉπ π + πΉπ π π¨π π½π = π½πΊ π + πΉ π + πΰ΅πΉ π π½πΊ = π°π πΉπ Rif is therefore, π½π = π¨π π½πΊ π½π π½π πΉππ = = π½πΊ π°π ΰ΅πΉ π π½π = π½πΊ + π½ππ π¨π πΉππ = πΉπ π + π+ πΉπ ΰ΅πΉ π π½ππ = πΉπ π + π·π π¨π πΉπ ≅ π½ πΉπ + πΉ π π 29 Feedback & Stability 30 Feedback & Stability Op-Amp Shunt-Series Feedback Circuit • SELF READING 31
