Feedback & Oscillator

A negative feedback amplifier (or feedback amplifier) is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal.electronic amplifiernegative feedback The applied negative feedback improves performance (gain stability, linearity, frequency response, step response) and reduces sensitivity to parameter variations due to manufacturing or environment.

An idealized negative feedback amplifier as shown in the diagram is a system of three elements (Fig. above): An amplifier with gain A OLgain A feedback network 'β', which senses the output signal and possibly transforms it in some way (for example by attenuating or filtering it)attenuating filtering A summing circuit that acts as a subtractor (the circle in the figure), which combines the input and the transformed output

Fundamentally, all electronic devices that once provided power gain (e.g., vacuum tubes, bipolar transistors, MOS transistors) are nonlinear.vacuum tubesbipolar transistorsMOS transistorsnonlinear Negative feedback trades gain for higher linearity (reducing distortion), and can provide other benefits.gaindistortion

If not designed correctly, amplifiers with negative feedback can become unstable, resulting in unwanted behavior such as oscillation. oscillation The Nyquist stability criterion developed by Harry Nyquist of Bell Laboratories is used to study the stability of feedback amplifiers.Nyquist stability criterionHarry NyquistBell Laboratories

Pros of fb. amplifier Can increase or decrease input impedance (depending on type of feedback) Can increase or decrease output impedance (depending on type of feedback) Reduces distortion (increases linearity) Increases the bandwidth Desensitizes gain to component variations Can control step response of amplifier

Step response? A typical step response for a second order system, illustrating overshoot, followed by ringing, all subsiding within a settling time.overshootringingsettling time

History Harold Stephen Black invented the negative feedback amplifier while he was a passenger on the Lackawanna Ferry (from Hoboken Terminal to Manhattan) on his way to work at Bell Laboratories (located in Manhattan instead of New Jersey in 1927) on August 2, 1927 (US patent 2,102,671, issued in 1937).Harold Stephen Black Black was working on reducing distortion in repeater amplifiers used for telephone transmission.distortion

On a blank space in his copy of The New York Times, he recorded the diagram found in Figure 1, and the equations derived below. On August 8, 1928, Black submitted his invention to the U. S. Patent Office, which took more than nine years to issue the patent. Black later wrote: "One reason for the delay was that the concept was so contrary to established beliefs that the Patent Office initially did not believe it would work."

Cons of fbA May lead to instability if not designed carefully Amplifier gain decreases Input and output impedances of a negative feedback amplifier (closed-loop amplifier) become sensitive to the gain of an amplifier without feedback (open-loop amplifier)—that exposes these impedances to variations in the open loop gain, for example, due to parameter variations or nonlinearity of the open-loop gain

Fb connection types Both voltage and current can be fed back to the input either in series or parallel. 1. Voltage-series feedback ( Fig a). 2. Voltage-shunt feedback ( Fig b). 3. Current-series feedback ( Fig c). 4. Current-shunt feedback ( Fig d).

voltage refers to connecting the output voltage as input to the feedback network; current refers to tapping off some output current through the feedback network. 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.

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.

What we want?  Typically, higher input impedance and lower output impedance are desired for most cascade amplifiers. Which combination can do it?  Both of these are provided using the voltage-series feedback connection. So lets concentrate first on this amplifier connection.

(a) Voltage-series fb Voltage refers to connecting the output voltage as input to the feedback network; Series refers to connecting the feedback signal in series with the input signal voltage

Figure 14.2(a) shows the voltage-series feedback connection with a part of the output voltage fed back in series with the input signal, resulting in an overall gain reduction. If there is no feedback (V f = 0), the voltage gain of the amplifier stage is

So, the overall voltage gain with fb, Eq. shows that the gain with feedback is the amplifier gain reduced by the factor (1 + βA). This factor will be seen also to affect input and output impedance among other circuit features.

If A >> 1, then A f ≈ 1 / β and the effective amplification (or closed-loop gain) A fb is set by the feedback constant β, and hence set by the feedback network, usually a simple reproducible network, –thus making linearizing and stabilizing the amplification characteristics straightforward.

If there are conditions where βA = −1,  the amplifier has infinite amplification –it has become an oscillator, and –the system is unstable.

The stability characteristics of the gain feedback product βA are often displayed and investigated on a Nyquist plot (a polar plot of the gain/phase shift as a parametric function of frequency).Nyquist plot A simpler, but less general technique, uses Bode plots.Bode plots

a) Volt-series

b) Volt-shunt fb

c) Current series

d) current-parallel

Practical volt-series feedback ckt using FET?

Volt –series using opAmp?

Using BJT?