Analog Simulation:Models for Operational Amplifiers.

Models for Operational Amplifiers

Device Model

There are no principal difficulties to prepare a circuit diagram of an integrated operational amplifier for a SPICE input. Figure 10.31 shows for instance the circuit diagram of the classical μA741 operational amplifier [10.6] from which the SPICE input can be derived immediately.

Figure 10.31 is called a device model. The difficulty in applying such a model lies in the model parameters of the 20 to 30 transistors being not normally known and not being able to determined by measurements involving output nodes only. Even if the IC manufacturer provides all model parameters the number of transistors is the prob- lem: if, for instance, filters consisting of several operational amplifiers are analysed one has to deal with a circuit of hundreds of transistors, which can result in convergence difficulties and excessive computing time.

ABM Models

Often it is not necessary to take all effects of an operational amplifier into account when interest is only in its analog behavior. The suitable models for this purpose are called ‘Analog Behavioural Models’ (ABM Models).

Ideal Operational Amplifier

To model an ideal operational amplifier a volt- age controlled voltage source with a gain of, e.g., 200,000 can be used. Even with finite input and output resistances one speaks of an ideal operational amplifier which is shown in fig. 10.32.

Analog Simulation-0136Analog Simulation-0137

Operational Amplifier with Saturation

If one wants to simulate oscillators using operational amplifiers one has to model saturation effects, otherwise the amplitude of the oscillating voltage would increase to infinity. Figure 10.33 shows the application of the ABM model ‘ETABLE’ for this purpose. By defining the values (−15, −15) (15, 15) saturation at the output to ±15 V is caused, as is shown in the simulated transfer curve fig. 10.34.

Analog Simulation-0139

Operational Amplifier with Frequency Response

When simulating active filters the frequency response of the operational amplifiers used also has to be taken into account. For this purpose a convenient possibility is given when applying the ABM model ‘ELAPLACE’. Figure 10.35 shows an example for the application where the Laplace transfer function is signified by two poles at 5 Hz and 2 MHz. Figure 10.36 shows the simulated frequency response with respect to magnitude and phase.

Analog Simulation-0138

Analog Simulation-0140

Macro Model of the Operational Amplifier

Figure 10.37 shows two operational amplifier models with 100 % feedback paralleled at their inputs. The first is the ABM model ‘ELAPLACE’ discussed above, the second is the library model μA741 to be found in the PSPICE version 8 [10.5].

Analog Simulation-0141

Figure 10.38 displays the frequency response with respect to magnitude of both models which show practically no difference.

If, on the other hand, the step response is of interest the differences are remarkable as is shown in fig.

10.39. The reason is to be found in the linear ABM model not being able to simulate the non-linear slew rate effect whereas this is possible with the library model of the μA741. This model is a so called macro model of the operational amplifier R1 and represents a compromise between the device 1 k and the ABM model. The idea behind this is to simulate as many effects of the real operational amplifier as possible with a minimum of non-linear components. In addition, the model parameters may be determined from data sheet information of the manufacturer [10.6]. Listing 10.1 shows the SPICE netlist of the macro model μA741 to be found in the library EVAL.LIB of the PSPICE evaluation version.

Detailed information regarding the different components can be found in [10.13]. Summing up, the following may be said: the input behavior is simulated by the differential amplifier with the  transistors Q1 and Q2. The other semiconductor elements are diodes which only serve to simulate saturation effects and do not affect the normal operation.

Analog Simulation-0142

The large gain of the operational amplifier is mainly represented by the current controlled cur- rent source FB, the controlled source GCM simulates the common mode gain. In [10.13] it was pointed out that there is an error in this kind of common mode simulation which is already to be found in the original paper [10.1] and in all PSPICE versions. It is wrong to take the common mode voltage from the resistor REE because this leads necessarily to an unwanted offset at the output as a result of a DC voltage drop in REE at the operating point. One has to derive the control- ling voltage of the source GCM directly from the common mode voltage at the input, i.e., from the arithmetic mean value of the input voltages.

In order to illustrate the macro model the slew rate simulations will be discussed. A step function at the (+) input saturates the transistor Q2 and the current IEE flows through RC2 = RC1. Therefore VA = IEE · RC1 and the voltage controlled current source GA charges the capacitor C2 with IEE. The slew rate is given by:

Analog Simulation-0143

Analog Simulation-0144

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