2. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Frequency response of an amplifier Decibel power gain Decibel voltage gain Impedance matching Decibels above a reference The Miller effect

3. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Frequency response A graph of voltage gain vs. input frequency An ac amplifier has a lower and upper cutoff frequency A dc amplifier has only an upper cutoff frequency

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Coupling and bypass capacitors produce the lower cutoff frequency Internal transistor capacitance and stray wiring capacitance produce the upper cutoff frequency

5. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 0.707 A V(mid) AVAV f A V(mid) The frequency response curve of an ac amplifier f1f1 f2f2 10f 1 0.1f 2 The cutoff frequencies Also called the half-power frequencies The midband The gain is maximum in the midband.

6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Decibel power gain Defined as 10 times the common logarithm of the power gain When power gain increases by a factor of 2, the decibel power gain increases by 3 dB When power gain increases by a factor of 10, the decibel power gain increases by 10 dB

7. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Decibel voltage gain Defined as 20 times the common logarithm of the voltage gain When voltage gain increases by a factor of 2, the decibel voltage gain increases by 6 dB Total dB voltage gain of cascaded stages equals the sum of decibels of each stage

8. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Impedance matching Produces maximum power transfer In an impedance-matched system, the decibel power gain and the decibel voltage gain are equal

9. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Decibels above a reference Two popular references are the milliwatt and the volt Decibels with the 1 milliwatt reference are labeled dBm Decibels with the 1 volt reference are labeled dBv

10. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The Miller effect A feedback capacitor from the output to the input of an inverting amplifier is equivalent to two capacitors Refers to the input capacitance being (inverting amp) A V + 1 times the feedback capacitance

11. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Inverting amplifier A V v in v out Inverting amplifier A V v in v out C C in C out Miller equivalent circuit Inverting amplifier with feedback capacitor C in = C(A V +1) C out = C A V +1 AVAV

12. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Frequency compensation Most op amps are internally compensated to prevent oscillations One dominant internal compensation capacitor rolls off the gain at 20 dB/decade IC capacitors are limited to the pF range The Miller effect makes the internal compensation capacitor equivalent to a much larger capacitor

13. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Combined frequency effects The input coupling, output coupling, and emitter bypass capacitors each produce a cutoff frequency. One is usually dominant (the highest frequency) and produces a rolloff of 20 dB/decade as frequency decreases. When the next cutoff is reached, the gain rolloff increases to 40 dB/decade. When the third is reached, it becomes 60 dB/decade.

14. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Bypass circuits The base bypass circuit contains the internal base-emitter capacitance (C’ e ) and the Miller capacitance due to the internal collector-base feedback capacitance (C’ c ) The collector bypass circuit contains the Miller capacitance and the stray (wiring) capacitance.