1. 1 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:

2. 2 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)

3. 3 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

4. 4 Closed-Loop Bandwidth But we know that, and Therefore, This same formula applies to a non-inverting as well as an inverting amplifier   Substituting,

5. 5 Gain Bandwidth Product Note that you are trading off the high gain of the op-amp for a higher bandwidth

6. 6  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

7. 7 Bandwidths of Inverting and Noninverting Amplifiers Closed loop bandwidth Closed loop gain for non-inverting amp Closed loop gain for inverting amp Closed loop bandwidth

8. 8 Output Voltage Swing Output Current Limits Large Signal Operation Output voltage cannot exceed the maximum supply voltage. It also depends on the type of op-amp design to some extent. Clipping of the output voltage occurs when either the output voltage or the output current reaches its limit