Università degli Studi di Roma Tor Vergata Dipartimento di Ingegneria Elettronica Analogue Electronics Paolo Colantonio A.A. 2056
Operational amplifiers (op amps) Operational amplifiers (op amps) are among the most widely used building blocks in electronics They are integrated circuits (ICs) Package: DIL (or DIP) or SMT (or SMD) DIL (or DIP) Dual in line package SMT Surface mount technology SMD Surface mount device 2 23
Operational amplifiers (op amps) A single package will often contain several op amps 3 23
An ideal operational amplifier An ideal op amp would be an ideal voltage amplifier and would have: Av =, Ri = and Ro = 0 Equivalent circuit of an ideal opamp It is typically realized by DC coupled amplifier with a very high open loop gain. It can be biased in a symmetric way (i.e. V CC and V CC ) or with a single positive bias value (V CC ) depending if the output signal should be varied around zero or not. 4 23
Operational Amplifiers Ideal characteristics Voltage Gain infinite A d = Input impedance infinite Z in = Output impedance null Z o =0 Common Mode Rejection Ratio (CMRR) infinite Bandwidth infinite 0 2 In an ideal op amp it follows that the input current is null If the output voltage is finite then the input voltage (V V ) is null (virtual earth) The amplifier performance are not depending on the loading conditions The bias voltages represent the minimum and maximum output voltage values Being Av=, the output voltage of an op. amp. in an open loop configuration can assume only one of the two saturating values (V CC or V CC ) The use of ideal components makes the analysis of these circuits very straightforward 5 23
Inverting amplifier I 2 R I v i Since the gain is assumed infinite, if is finite the input voltage V i must be zero 0 Since the input resistance of the op amp is, its input current must be zero 6 23
An inverting summing amplifier Consider the circuit with more inputs R 3 Since the input resistance of the op amp is, its input current must be zero, and hence 0 Since the input voltage is null (earth ground circuit) V 3 R I 3 I 2 I R 4 I 4 V 4 0 thus The output signal is a weighted sum of the input signals (considering R i as resistances). 7 23
Level shifter Summing amplifiers make convenient level shifters. Assuming that an input signal has to be shifted around a fixed level V L R I 2 I R 3 I 3 V 3 By assuming The input signal is transferred to the output with gain, but shifted of a fixed value V L. If a trimmer is used for R2, the offset level V L can be fine controlled. 8 23
Inverting amplifier with A v Mantaining the assumption of a null input current: R I 2 I v i Replacing into the former equation: The finite gain A implies a difference with respect to the theoretical gain ( /R ) which is larger as lower is A. 9 23
Non inverting amplifier Assuming a null input voltage and current thus R I 2 I We can observe that assuming =0 or R = the amplifier gain becomes unitary. Thus we can realize an ideal buffer stage ideale (R in =, R o =0, A v =) by using one of the two following configurations: =0 R R = 0 23
A current to voltage converter 23
A differential amplifier (or subtractor) By using both the input ports of the opamp and by using the superposition principle: R I Assuming the earth ground principle (V =V ): R 3 R 4 NI V 3 Making a mathematical rearrangement 2 23
A differential amplifier (or subtractor) Assuming v 2 v, thus (v 2 v )/2 v Differential mode amplification 2 Common mode amplification R R 3 R 4 I NI V 3 If 3 23
Differential amplifier for instrumentation Computing the input impedance 2 If a large A d is required, then /R is high, which in turns implies R low and thus R id too low 4 23
New configuration Differential amplifier for instrumentation R used to control the gain A d 5 23
Differential amplifier for instrumentation Applying the superposition principle on the first part of the circuit 2 2 2 2 6 23
Integrator and differentiator In an inverting amplifier we saw that: i C i R R C a) integrator For the scheme a) For the scheme b) b) differentiator Very high sensitivity to low frequencies (integrator) or high frequencies (differentiator) Low values of v i could results in very high v o levels, resulting in a circuit failure 7 23
Actual integrator and differentiator In order to solve the frequency issues the previous circuits are modified as in the following C C R V V 2 b) differentiator a) integrator R The insertion of a resistor modifies the frequency behavior avoiding the answer to increase indefinitely towards infinity Practically the bandwidth has been modified in the upper (case a) or in the lower (case b) frequency range 8 23
Actual integrator R C 2 a) integrator Comparing the result with the response of a Low Pass RC filter A v 3dB 2 C f s log(f) 45 f s A v 80 90 log(f) The real integrator behaves like a Low Pass RC filter The group C limits the opamp bandwidth, which output is proportional to the input up to f H, while for f>f H it integrates the input signal. 9 23
Actual differentiator R C b) differentiator 2 Comparing the result with the response of a High Pass RC filter 3dB 45 A v f i log(f) 270 C 2 80 f s log(f) The real differentiator behaves like a High Pass RC filter The group R C limits the opamp bandwidth, which output is the differentiation of the input up to f L, while for f>f L it is simply proportional to the input signal. 20 23
Limitation of the opamp bandwidth The previous schemes can be combined to limit the opamp bandwidth as reported in the following scheme C 2 2 R C 2 (f H f L ) is the bandwidth of the resulting amplifier Bandwidth log(f) 2 23
Frequency behaviour of opamp Actual opamp have a finite gain which is also frequency dependent Simplified approximation For >> b Unity gain bandwidth 22 23
Opamp limitations Maximum voltage swing: the output voltage is limited between the maximum and minimum bias voltages Slew rate: the output voltage time variation is limited 23 23