1. 1 Amplifiers

2. Equivalent Circuit of a Voltage Amplifier G vo V i IoIo RoRo VoVo ViVi -- ++ RiRi IiIi Amplifier ViVi VoVo (a) Black Box Representation (b) Equivalent Circuit V o = G vo V i G vo = open-circuit voltage gain, ie gain with no load R i = input resistance R o = output resistance

3. Equivalent Circuit of a Voltage Amplifier with Input Signal Source and Output Load 3 - + - - + + IiIi IoIo RoRo RsRs G vo V i RiRi RLRL ViVi VsVs VoVo

4. Amplifiers in Cascade 4 Amplifier 2 Amplifier 1 V o1 ViVi VoVo

5. Example: An integrated circuit amplifier has an open-circuit voltage gain of 60dB, an input resistance of 90kΩ and an output resistance of 50Ω. Its input is connected to a 1mV (rms) signal source with an internal resistance of 10kΩ and its output to a 450Ω resistive load. Determine the rms value of the output voltage across the load. 5

6. Circuit Symbol for an Operational Amplifier 6 Non-Inverting Input Inverting Input Negative Supply Positive Supply - + - + VsVs VsVs V1V1 V2V2 VoVo V o = +AV 1 - AV 2 = A(V 1 - V 2 ), A = open-loop gain If V 2 = 0, V o = +AV 1 --- non-inverting mode (output is in phase with the input) If V 1 = 0, V o = -AV 2 --- inverting mode (output is 180 o out of phase with the input)

7. ‘Black Box’ Representation of an Op-Amp 7 - + V d = V 1 – V 2 VdVd V2V2 V1V1 VoVo RiRi RoRo AV d Frequency (Hz) Open-Loop Voltage Gain 10 6 10 5 10 4 10 3 10 2 10 1 10 3 10 5 10 6 10 7 10 8 0 10 4 10 2 The main characteristics of an operational amplifier are: A very high voltage gain, called the open-loop gain. This is typically in the range 10 5 – 10 6 at DC and low frequencies, but decreases with frequency as shown. A very high input resistance R i between the inverting and non-inverting input terminals, which is typically of the order 10 12 Ω. A very low output resistance R o which is typically 100 Ω.

8. THE IDEAL OP-AMP 8 - + V o =A (V 1 – V 2 ) V2V2 V1V1 Infinite input resistance (R i =  ), ie the op-amp does not draw any current from any source connected to it. Zero output resistance (R o = 0 Ω). That is, the output acts as an ideal voltage source. Infinite open-loop gain (A =  ). The properties of an ideal op-amp are:

9. Op-Amp Inverting Amplifier 9 - + P i2i2 i1i1 V2V2 V1V1 V in VoVo R2R2 R1R1 Because of the large open-loop voltage gain (ideally infinite) of the operational amplifier, the voltage at point P must be very small if the amplifier output voltage is to remain within reasonable limits. Consequently, point P is virtually at zero volts, ie at ground or earth potential, and it is often referred to as a ‘virtual ground’ or ‘virtual earth’. Due to the very high input resistance of the op-amp between its inverting (-) and non-inverting (+) terminals, we can assume that a negligible current flows into the input terminals of the amplifier.

10. Op-amp Non-Inverting Amplifier 10 Due to the very large gain of the op-amp V 2  V 1 = V in - + i i R2R2 R1R1 P v in v1v1 v2v2 vovo

11. Voltage Follower or Buffer Amplifier 11 - + v in vovo

12. Summing Amplifier Circuit 12 - + i i1i1 i2i2 v2v2 v1v1 vovo RFRF R R P