Operational Amplifier with Capacitive Load

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Operational Amplifier with Capacitive Load

An Operational Amplifier (op-amp) is a differential voltage amplifier with a wide range of applications in analog electronics. This example shows how to model an operational amplifier connected to a feedback loop and a capacitive load and calculate the transient step response of the entire system. The basic op-amp model used here is implemented as an equivalent linear subcircuit in the Electrical Circuit interface in COMSOL Multiphysics. The latter is partially based on the SPICE format originally developed at Berkeley University (Ref. 1).

Model Definition

The op-amp subcircuit is described by the following lines in a SPICE netlist:

.SUBCKT OPAMP p n out gnd

RIN p n 100000.0

EGAIN 1 gnd p n 100000.0

RP 1 2 1591549.4309189531

CP 2 gnd 1.0E-9

EBUFFER 3 gnd 2 gnd 1.0

ROUT 3 out 100.0

The different stages are:

•

An input with high impedance: RIN.

•

A high gain differential amplifier: EGAIN.

•

A single-pole low-pass filter: RP and CP.

•

An output buffer with unity gain: EBUFFER and ROUT.

The op-amp subcrcuit instance is then inserted into the main circuit:

XOPAMP 1 2 3 0 OPAMP

CLOAD 3 0 1.0E-8

Here the voltage source is indicated as being constant at 0.5V whereas in the model a voltage step of 0.5V is applied at t=0. A resistive feedback loop is provided through the resistors R1 and R2 and the amplifier output is terminated to ground via a capacitive load CLOAD.

Results and Discussion

The model is simulated for 10μs with data output every 0.05μs. The internal dynamics of the op-amp interacts with the feedback network causing ringing in the output signal.

Figure 1: The output voltage of the op-amp as a function of time.

1. The SPICE home page, http://bwrc.eecs.berkeley.edu/Classes/IcBook/SPICE.

ACDC_Module/Tutorials/opamp_capacitive_load

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

In the tree, select .

3

4

5

In the tree, select .

6

Global Definitions

Start by defining the parameters to be used in the model.

1

In the window, under click .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Value	Description
OPAMP_RIN	100[kohm]	1E5 Ω	Op-amp input resistance
OPAMP_GAIN	1e5	1E5	Op-amp gain
CLOAD	10[nF]	1E-8 F	Capacitive load
R1	470[ohm]	470 Ω	Feedback resistance 1
R2	4700[ohm]	4700 Ω	Feedback resistance 2
OPAMP_P	100[Hz]	100 Hz	Op-amp pole frequency
OPAMP_ROUT	100[ohm]	100 Ω	Op-amp output resistance

Add a step function and a variable defining the voltage step used to drive the model.

In the toolbar, click

and choose .

1

In the toolbar, click

and choose .

2

In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Unit	Description
VIN	.5[V]*step1((t-.05[us])/1[us])	V	Input voltage

Electrical Circuit (cir)

Now, define the circuit. Start by defining the subcircuit for the op-amp.

1

In the window, under right-click and choose .

2

In the window for , type OPAMP in the text field.

3

Locate the section. Click

.

4

5

In the table, enter the following settings:


Node names
p
n
out
gnd

1

In the toolbar, click

.

2

In the window for , type Resistor RIN in the text field.

3

In the text field, type RIN.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	p
n	n

5

Locate the section. In the R text field, type OPAMP_RIN.

Voltage-Controlled Voltage Source EGAIN

1

In the toolbar, click

.

2

In the window for , type Voltage-Controlled Voltage Source EGAIN in the text field.

3

In the text field, type EGAIN.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	1
n	gnd
measure (+)	p
measure (-)	n

5

Locate the section. In the text field, type OPAMP_GAIN.

1

In the toolbar, click

.

2

In the window for , type Resistor RP in the text field.

3

In the text field, type RP.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	1
n	2

5

Locate the section. In the R text field, type 1/(2*pi*OPAMP_P*1[nF]).

1

In the toolbar, click

.

2

In the window for , type Capacitor CP in the text field.

3

In the text field, type CP.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	2
n	gnd

5

Locate the section. In the C text field, type 1[nF].

Voltage-Controlled Voltage Source EBUFFER

1

In the toolbar, click

.

2

In the window for , type Voltage-Controlled Voltage Source EBUFFER in the text field.

3

In the text field, type EBUFFER.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	3
n	gnd
measure (+)	2
measure (-)	gnd

1

In the toolbar, click

.

2

In the window for , type Resistor ROUT in the text field.

3

In the text field, type ROUT.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	3
n	out

5

Locate the section. In the R text field, type OPAMP_ROUT.

Voltage Source VIN

Proceed to add the main circuit, start by adding the voltage source.

1

In the toolbar, click

.

2

In the window for , type Voltage Source VIN in the text field.

3

In the text field, type VIN.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	1
n	0

5

Locate the section. In the vsrc text field, type VIN.

Subcircuit Instance XOPAMP

Add the subcircuit instance for the opamp.

1

In the toolbar, click

.

2

In the window for , type Subcircuit Instance XOPAMP in the text field.

3

In the text field, type XOPAMP.

4

Locate the section. From the list, choose .

5

In the table, enter the following settings:


Local node names	Node names
p	1
n	2
out	3
gnd	0

Resistor 1 (R1)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the table, enter the following settings:


Label	Node names
p	2
n	0

4

Locate the section. In the R text field, type R1.

Resistor 2 (R2)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the table, enter the following settings:


Label	Node names
p	2
n	3

4

Locate the section. In the R text field, type R2.

Capacitor CLOAD

1

In the toolbar, click

.

2

In the window for , type Capacitor CLOAD in the text field.

3

In the text field, type CLOAD.

4

Locate the section. In the table, enter the following settings:


Label	Node names
p	3
n	0

5

Locate the section. In the C text field, type CLOAD.

Volt Meter 1 (vm1)

In order to see the output voltage, a voltmeter is added.

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the table, enter the following settings:


Label	Node names
p	3
n	0

Step 1: Time Dependent

1

In the window, under click .

2

In the window for , locate the section.

3

4

In the dialog box, type 0.05[us] in the text field.

5

In the text field, type 10[us].

6

7

In the toolbar, click

.

Probe Plot Group 1

The output voltage appears as a probe plot.

Finally add a model thumbnail image.

1

In the window, click the root node.

2

In the root node’s window, locate the section.

3

Find the subsection. Click .