PC2181E Amplifiers and Feedback
A 3-day Laboratory-based Course

Simple Amplifier

A simple amplifier can be represented like this.
Vout = A Vin.
A is the "open loop" amplification or gain. (A is complex to represent both magnitude |A| and phase shift arg A.)

Usually we want:

  • the ability to control the gain;
  • independence of frequency (over some range or bandwidth);
  • high input impedance (to avoid drawing too much current from the source of Vin);
  • low output impedance (so that a load does not affect Vout too much).
  • Feedback

    By adding all or part of the output back to the input one can control the overall gain.
    V' = Vin + beta Vout   and   Vout = A V',
    where we have introduced the (complex) feedback factor, beta, the proportion of the output added to the input. Eliminating V', one gets
    Vout = Vin A / (1 - beta A).
    Thus the "overall" gain of the circuit is A' = Vout/Vin = A / (1 - beta A).
  • If |beta A| >> 1, A' = - 1 / beta (approx.).  It usually turns out that beta is much easier to manufacture reproducibly than A. But by makine |A| large, we can produce an overall gain which is independent of A.
  • It is only stable if Re beta < 0 (negative feedback).
  • Negative feedback increases the overall input impedance, decreases the overall output impedance and increases the overall bandwidth relative to their open loop values. In other words, negative feedback improves all the important characteristics of an amplifier.
  • Differential or Operational Amplifier

    The differential or operational amplifier is an extremely versatile invention. With it we can implement the idea of feedback introduced above. It is the basis of a very flexible and practical solution to our needs. In a variety of configurations, we can, within limits, choose gain, bandwidth, impedance and can make oscillators, summers, etc. Its basic characteristics are:
  • Vout = A (V+ - V-)
  • very high open loop gain (typically, |A| ~ 105);
  • good bandwidth (typically 1 MHz);
  • very high input impedance (typically 10 MOhms);
  • low output impedance (typically 100 Ohms - don't connect loads with lower impedance than this!).
  • Non-inverting Amplifier

    In the circuit shown, the negative input is constrained to be
    V- = VoutR1 / (R1 + R2).
    From above we also have
    Vout = A (Vin - V-)
    and eliminating V-, we obtain the overall gain,
    Vout/Vin = A' = A / (1 - beta A),
    where, in this case, beta = -R1 / (R1 + R2).

    The differential amplifier has allowed us to add - or in this case subtract - some portion of the output from the input. This circuit is an example of negative feedback.

    If |A| is large,

    A' = -1/beta (approx.) = (R1 + R2) / R1.
    Thus, it is easy to control the overall gain by choosing the resistors. Resistors are easy to make, stable and reproducible. Even if the open loop gain, A, has characteristics that are somewhat unknown or variable, as long as |A| is large, the overall gain is well defined. Note that this approximation is good even if A is complex, i.e., introduces a phase shift; the overall gain is real, i.e., no phase shift, since beta is real (in this case).

    Although the overall gain depends only on the ratio (R1 + R2) / R1, it is important to choose R1, R2 large enough that they do not constitute a serious load on the output and not too large that they cannot supply enough current to the input. This means they must have values comfortably between the open loop input impedance, 10 MOhms, and the open loop output impedance, 100 Ohms.  Let us say between 1 kOhm and 100 kOhms.

    Inverting Amplifier

    Make a similar analysis of this circuit. What is the overall gain? What is its input impedance?

    Day 1 - Negative Feedback

    The first day of laboratory work will be devoted to building amplifiers with negative feedback and measuring some of their characteristics. ((*)Starred measurements are part of the "bonus" component of our "satisfactory + bonus" scheme.)
    1. Build a non-inverting amplifier with an overall gain of about 10. Good values of feedback resistors would be R1 = 3 kOhm, R2 = 30 kOhms. Consult the script, pages 2 and 3, for details of the 741 and practical advice.
    2. Find the 3 dB frequency of a x100 amplifier. Choose values of R1 and R2.
    3. (*)Find the 3 dB frequency of a "total feedback" unit-gain circuit (Vout connected directly and only to V- - shown above)
    4. Build an inverting amplifier with R1 = 3 kOhm, R2 = 30 kOhms. Measure its gain at 1 kHz and measure its 3 dB frequency.
    5. (*)Build this circuit (with 2 inputs, V1 and V2).  What does it do?
    6. Be prepared to demonstrate and explain your results to a demonstrator - this will contribute to the daily assessment.
    For experimental details and suggestions, see script.

    John Allison
    13th Sep 2001