1. Non-Ideal Characteristics Input impedance Output impedance Frequency response Slew rate Saturation Bias current Offset voltage

2. Input and Output Impedances Ideal model assumes: R IN is infinite R OUT is zero In real life: R IN > 1 M  R OUT < 100 

3. Input Impedance In either configuration, voltage across R IN will be small (ideally zero) if A 0 is high. Current through R IN should, therefore, be small. Effect will be more notable for non-inverting configuration where ideal input current is zero.

4. Non-Inverting Amplifier

5. Output Impedance To calculate output impedance: Imagine the input voltage is zero. The output voltage should also be zero. The output looks like just R OUT connected to ground. To calculate/measure R OUT, connect a signal generator to the output and calculate/measure the current.

6. Output Impedance With the input set at zero, the equivalent circuits for non-inverting and inverting configurations are identical. Actual output impedance is V OUT /I.

7. Calculating Actual Output Impedance But,

8. We know that A 0 >> 1 and that R OUT is either small or comparable with R 1 and R 2. Typically, R OUT appears to be reduced by several orders of magnitude.

9. Input/Output Impedance Summary Negative feedback is very good at compensating for non-ideal properties of the amplifier. The effects of finite input impedance and non-zero output impedance are greatly reduced thanks to negative feedback. Eg. Using a 741, an amplifier with a gain of 10 has R OUT of around 100  x 10/10 5 = 10 m  ! NB. Negative feedback will not work so well unless the open-loop gain of the op-amp is very large. Reasonable at d.c. and low frequencies. At higher frequencies…

10. Frequency Response The open-loop gain of an op-amp features in the calculations for: Voltage gain Input impedance Output impedance We assumed it was very large (near infinite) True at low frequencies Not so at higher frequencies

11. Open-Loop Gain vs. Frequency First order approximation:

12. Effects of Frequency Response Ideally, gain = 10

13. Frequency Response (cont) Constant, K, depends on the op-amp. For a 741 it is around 2  10 6. i.e. A first order low- pass filter, cut-off frequency of 100 kHz.

14. Gain-Bandwidth Product Cut-off frequency multiplied by mid-band gain is always the same value. This is the gain-bandwidth product (1 MHz in this case).

15. Frequency Response Summary It is impossible to design an amplifier whose gain exceeds A 0 (f) at any frequency. At high frequencies, gain is limited by A 0 which typically rolls-off at 20dB-decade. The cut-off frequency is The intersection of the low and high frequency asymptotes The –3dB point The gain-bandwidth product divided by the mid-band gain

16. Slew Rate There is a maximum rate of change associated with the output of an op-amp. The Slew Rate. Typical value for a 741 is 0.5 V/  s.

17. Effect of Slew Rate on a Sine Wave For a sine wave output voltage of amplitude, A, and frequency, f: Rate of change of the output voltage is: To avoid slew rate limiting:

18. Full Power Bandwidth If the amplitude of the sine wave output is just below the saturation level, the maximum frequency that an undistorted SINE WAVE output can be obtained is often known as the full power bandwidth. E.g. 741 with saturation levels of ±13.5 V: NB. More about saturation next time…

19. Summary Real op-amps deviate from the ideal model in many ways. Negative feedback automatically compensates for many of these. Most of the time, therefore, the ideal model works pretty well… …except under extreme conditions. NB. Saturation comes up next time as an introduction to comparators.