The characteristics of general feedback amplifiers can be expressed in terms of the two-port model parameters for the individual open-loop amplifier and feedback network. Analysis of each of the four different interconnections of the amplifier and feedback network uses a particular set of two-port parameters: series-shunt feedback uses the h-parameters; shunt-shunt feedback uses the y-parameters; shunt-series feedback uses the g-parameters; and series-series feedback uses the z-parameters.
Series feedback places ports in series and increases the overall impedance level at the series-connected port. Shunt feedback is achieved by placing ports in parallel and reduces the overall impedance level at the shunt-connected port.
Before applying the methods, we must ensure that the amplifier and feedback networks can be properly represented as two-ports. Transistor realizations of series-shunt and shunt-shunt feedback amplifiers can readily be analyzed using h- and y-parameter descriptions,respectively. However, care must be exercised in the analysis of circuits that involve series feedback at the output port. Amplifiers in the shunt-series and series-series feedback circuit soften cannot be represented as two-ports, particularly when we try to calculate output resistance.
The loop gain plays an important role in determining the characteristics of feedback amplifiers. For theoretical calculations, the loop gain can be found by breaking the feedback loop at some arbitrary point and directly calculating the voltage returned around the loop. However, both sides of the loop must be properly terminated before the loop-gain calculation is attempted.
When using SPICE or making experimental measurements, it is often impossible to break the feedback loop. The method of successive voltage and current injection is a powerful technique for determining the loop gain without the need for opening the feedback loop.
Whenever feedback is applied to an amplifier, stability becomes a concern. In most cases, a negative or degenerative feedback condition is desired. Stability can be determined by studying the characteristics of the loop gain T(s) = A(s)β(s) of the feedback amplifier asa function of frequency, and stability criteria can be evaluated from either Nyquist diagrams or Bode plots.
In the Nyquist case, stability requires that the plot of T(jω) not enclose the T = -1 point.
On the Bode plot, the asymptotes of the magnitudes of A(jω) and 1/β(jω) must not intersect with a rate of closure exceeding 20 dB/decade.
Phase margin and gain margin, which can be found from either the Nyquist or Bode plot, are important measures of stability.
In circuits called oscillators, feedback is actually designed to be positive or regenerative so that an output signal can be produced by the circuit without an input being present. The Barkhausen criteria for oscillation state that the phase shift around the feedback loop must be an even multiple of 360° at some frequency, and the loop gain at that frequency must be equal to 1.
Oscillators use some form of frequency-selective feedback to determine the frequency of oscillation; RC and LC networks and quartz crystals can all be used to set the frequency.
Wien-bridge and phase-shift oscillators are examples of oscillators employing RC networks to set the frequency of oscillation.
Most LC oscillators are versions of either the Colpitts or Hartley oscillators. In the Colpitts oscillator, the feedback factor is set by the ratio of two capacitors; in the Hartley case, a pair of inductors determines the feedback.
Crystal oscillators use a quartz crystal to replace the inductor in LC oscillators. A crystal can be modeled electrically as a very high Q resonant circuit, and when used in an oscillator,the crystal accurately controls the frequency of oscillation.
For true sinusoidal oscillation, the poles of the oscillator must be located precisely on the jω axis in the s-plane. Otherwise, distortion occurs. To achieve sinusoidal oscillation,some form of amplitude stabilization is normally required. Such stabilization may result simply from the inherent nonlinear characteristics of the transistors used in the circuit, or from explicitly added gain control circuitry.
