Operational Amplifier model.

The operational amplifier, or OpAmp, is used to create an analog control for switched mode power supplies. Important parameters are the DC gain and slew rate of the device. Also the bandwidth at unity gain gives information about the performance of the Opamp at higher frequencies.

What model is required
For the Opamp there are basically two models. The static model includes the DC gain and the supply voltage limits of the output. The dynamic model includes the dynamics such as slew rate and bandwidth. The static model is preferred when simple control circuits are designed, where the dynamics of the Opamp are not influencing the dynamic behavior of the circuit. The dynamic model is required when the slew rate and bandwith of the Opamp have an influence on the characterisitcs of the circuit.

Static transfer function
The static transfer function for the Opamp is equal to:

V_o = DC_gain ·( V₊ - V_-)

The output voltage is limited between the supply voltages. The input impedance is modeled by R_in and is placed between the non-inverting and inverting input. The output impedance R_o limits the maximum current that can be drawn from the Opamp.

Dynamics
The dynamics of the Opamp are defined by the parameters slew-rate and unity bandwidth. The slew rate is given in volts per second, (multiply the slew rate by 1e6, if the value is given in volts/microsecond) and defines how fast the output voltage rises when a large input voltage is applied between the inputs of the Opamp. The unity bandwith defines the frequency when the gain of the opamp equals 1. Simply put, for DC, the dc gain of the Opamp is equal to DC_gain, but this gain is decaying with increasing frequency with -20dB per decade. At the unity bandwith frequency, the gain equals 1. The input capacitance is modeled by C_in and is placed between the non-inverting and inverting input.

Overview of the parameters
The parameters for the Opamp are summarized in the following table. Default values for the parameters are given. The output voltage limit values are defined by the voltage sources connected to the positive and negative supply terminals of the Opamp. Since these are circuit nodes, circuit voltage sources have to be applied and connected to the supply terminals.

OpAmp Static Parameters

Parameter	Default	Function
DCgain	100k	DC gain of the opamp
Rin	2MEG	Input resistance between the inverting and non-inverting input
Ro	75	Output resistance limiting the maximum current from the Opamp

OpAmp Dynamic Parameters

Parameter	Default	Function
Unity Bandwidth Gain	1MegHz	Open loop gain of the opamp equals 1 at this frequency
Cin	14pF	Input capacitance between the inverting and non-inverting input
Slew Rate	6e6	Slew Rate of the opamp in volts per second.