NONIDEAL OP AMP CIRCUITS

Objective of Lecture Describe the impact of real operational amplifiers on the models used in simulation and on the design approaches that have to be used. The output voltage of the amplifier is limited by the values of the power supplies. and current does enter the two input terminals The open-loop gain, A OL, of an op amp is not infinite. The gain of an op amp is dependent on the frequency of the signal. The slew rate of the op amp can cause oscillations rather than amplification, particularly when the amplifier gain is high.

Inverting Amplifier: Voltage Supplies isis ifif V+ = 15V V – = -10V i i 1 = 0 i 2 = 0

Example #1 (con’t) i 1 = 0 i 2 = 0isis ifif V+ = 15V V – = -10V i

Example #1 (con’t) i 2 = 0 i 1 = 0 isis ifif i

Example #1 (con’t) Since = -10 If V S = 0V, then V o = -10(0V) = 0V If V S = 0.5V, then V o = -10(0.5V) = -5V If V S = 1V, then V o = -10(1V) = -10V If V S = 1.1V, then V o = -10(1.1V) < V –, V o = -10V If V S = -1.2V, then V o = -10(-1.2V) = +12V If V S = -1.51V, then V o = -10(-1.51V) > V +, V o = +15V

Example #1 (con’t) Voltage transfer characteristic Slope of the voltage transfer characteristic in the linear region is equal to A V.

Rails Rails is another turn for the voltage supplies that power the operational amplifier. Rail-to-rail operation means that the output voltage can equal V + and V – at some points during its operation. 15 mV away from the voltage supplies is close enough to be called rail- to-rail.

LM 741 Operational Amplifier

Non-symmetrical Swing LM324 operational amplifier where V CCmax = 32 V

Inverting Amplifier: Finite R in isis ifif i isis ifif i i 1  0 i 2  0

isis ifif i Example #2 (con’t) Rin  ∞

Example #2 i1i1 i2i2 isis ifif i _vd+_vd+ A OL v d

Gain The gain of the amplifier is a function of R 1, R f, and R in.

Differential Voltage ( v d ) Since R in  ∞, then i 1 and i 2 are not equal to zero. That means that the voltages at the input terminals of the op amp are not equal V 1  V 2 v d  0 V Because of nonideal operation of the transistors inside the operational amplifier, v d  0 V even when V O = 0 V. Thus, there is an input offset voltage V 1 – V 2  0V. Some transistors have a pin that allow you to counterbalance this offset voltage.

Gain As the open-loop gain, A OL, of the op amp is finite, the closed-loop gain is a function R 1, R f, R in, and A OL.

Gain-Bandwidth Product Over a certain range of frequencies:

Slew Rate The speed at which the output voltage changes after a change in the input voltage. When the closed-loop gain is very large and the operating frequency is high, there is a chance that the output voltage will not follow the input voltage because it didn’t have time to reach the desired value before the input voltage changed. When this happens, it is possible for the op amp circuit to start oscillating.

Electronic Design Project The time-varying signal will be very small. To maximize the range of the mbed ADC that will be used to digitize the analogue signal, the amplifier will have to have a large gain. Because there will be significant noise on the signal that you want to detect, a bandpass filter will have to be designed that removes dc and very low frequency ac signals and removes high frequency noise. Given the frequency range that the bandpass filter must operate and that we would like the pulse meter to be powered by a battery, the resistors used in the filters will be large.

Op Amp Circuits to Consider Buffers (Voltage Followers) Isolate one subsystem from another Used in impedance matching Cascade Amplifiers Several amplifiers in series where the overall gain is the multiplication of the gain of each amplifier in series Active Filter An op amp with a combination of resistors and capacitors at the input termal and/or in the feedback loop. This is considered to be a filter (low, high, or bandpass) with gain. Passive filters (RC networks) are always lossy V O never is exactly equal to V in

Op Amp Circuits to Consider (con’t) Because there is only +9V, +5V, +3.3V, and ground available (the battery, the voltage regulator output, and the logical high voltage on the mbed), inverting amplifiers should not be used because at least half of the signal will be lost. Consider non-inverting amplifiers and difference amplifiers.