1. 1 The Operational Amplifier continued The voltage follower provides unity gain, however, the output impedance is changed according to the o/p impedance of the op- amp, which is very useful sometimes. Thus the op-amp acts as the buffer stage preventing the o/p load fluctuations to affect the i/p voltage signal.

2. 2 Non-inverting amplifier design: Effects of resistance choice A v = 10 = 1+R 2 /R 1 For v 0 = 10 V, output current is 1A Most op amps cannot handle such large current, so small R’s should be avoided Very large resistances tend to be unstable, and lead to coupling of unwanted signals especially at higher frequencies. Why?

3. Special circuits: Integrator and differentiators 3 Therefore, These circuits are useful for automobile ignition and fuel injection

4. 4 Op-Amp Imperfections in the linear range of operations Non-ideal properties in the linear range of operation Nonlinear characteristics DC offsets Input and Output Impedances  An Ideal op amp has infinite input impedance and zero output impedance  A Real op amp has finite input impedance and nonzero output impedance  For IC op amps made of BJTs open-loop input impedance is about 1 M   For IC op amps made of JFETs open-loop input impedance is about 10 12   Open loop output impedance is between 1 and 100    Closed loop impedances will be different, and can be chosen by proper resistors

5. 5 Characteristics of two popular Op Amps

6. 6 Op-Amp Imperfections in The Linear Range of Operations Gain and Bandwidth Limitations  Ideal op amps have infinite open-loop gain magnitude (A oL is infinite), but the gain of a real op amp is finite and a function of frequency  dc open-circuit differential voltage gain is typically between 10 4 to 10 6  The bandwidth is usually limited by the designer to prevent oscillations from feedback  by a process is called frequency compensation  A OL (f)- open-loop gain as function of frequency  A 0OL - dc open-loop gain  f BOL - open-loop break frequency  A OL (f) - constant up to f BOL then it rolls off at 20 dB/decade The open loop gain function of an op-amp usually has a single dominant pole and is given as:

7. 7 Gain-Bandwidth Limitations Assuming infinite input impedance and zero input current Voltage across resistor R 1 Thus, and Definition of open-loop gain Hence from (2.27) (2.27) Therefore, the closed-loop gain (2.26)

8. 8 In the limit of AOL tending to infinity, But For an ideal op amp This is the same result as before Op amp Closed-loop gain is given as, Putting We have, Definingand we have which is very similar in form to the open loop gain

9. 9 Closed-Loop Bandwidth But we know that and Therefore This same formula applies to a non-inverting as well as an inverting amplifier   Substituting,

10. 10 Gain Bandwidth Product Note that you are trading off the high gain of the op-amp for a higher bandwidth

11. 11  A 0CL A 0CL (dB) f BCL 10.99999004 MHz 0.19.999020400 kHz 0.0199.904040 kHz Closed-Loop Gain Versus Frequency Not that at f t the gain becomes 1