Operational Transconductance Amplifier

Behavioral representation of operational transconductance amplifier

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Libraries:
Simscape / Electrical / Integrated Circuits

Description

The Operational Transconductance Amplifier block provides a behavioral representation of an operational transconductance amplifier. A transconductance amplifier converts an input voltage into an output current. Applications include variable frequency oscillators, variable gain amplifiers and current-controlled filters. These applications exploit the fact that the transconductance gain is a function of current flowing into the control current pin.

To support faster simulation, the behavioral representation does not model the detailed transistor implementation. Therefore, the model is only valid when operating in the linear region, that is, where the device input resistance, output resistance, and transconductance gain all depend linearly on the control current, and are independent of input signal amplitude. The dynamics are approximated by a first-order lag, based on the value you specify for the block parameter Bandwidth.

Control Current

The control current pin C is maintained at the voltage that you specify for the Minimum output voltage. In practice, the Minimum output voltage equals the negative supply voltage plus the transistor collector-emitter voltage drop. For example, if the Minimum output voltage for a supply voltage of +-15V is -14.5, then to achieve a control current of 500μA, a resistor connected between the +15V rail and the control current pin must have a value of (15 - (-14.5)) / 500e-6 = 59kOhm.

Transconductance

The relationship between input voltage, v, and transconductance current, i_gm, is:

$$\begin{array}{l}v=v_{+}-v_{-}\\ i_{gm}=g_m\cdot v\\ g_m=\frac{g_{m0}\cdot i_c}{i_{c0}}\end{array}$$

where:

• v₊ is the voltage presented at the block + pin.

• v_– is the voltage presented at the block - pin.

• g_m is the transconductance.

• i_c is the control current flowing into the control current pin C.

• i_c0 is the reference control current, that is, the control current at which transconductance is quoted on the datasheet.

• g_m0 is the transconductance measured at the reference control current i_c0.

Therefore, increasing control current increases the transconductance.

Output Resistance and Determining Output Current

The output resistance, R_out, is defined by:

$$\begin{array}{l}{i}_{gm}+i_o=\frac{v_o}{R_{out}}\\ R_{out}=\frac{R_{out0}\cdot i_{c0}}{i_c}\end{array}$$

where:

• i_gm is the transconductance current.

• i_o is the output current, defined as positive if flowing into the transconductance amplifier output pin.

• i_c is the control current flowing into the control current pin C.

• i_c0 is the reference control current, that is, the control current at which output resistance is quoted on the datasheet.

• R_out0 is the output resistance measured at the reference control current i_c0.

Therefore, increasing control current reduces output resistance.

Input Resistance

The relationship between input voltage, v, across the + and - pins and the current flowing, i, is:

$$\begin{array}{l}\frac{v}{i}=R_{in}\\ R_{in}=\frac{R_{in0}\cdot i_{c0}}{i_c}\end{array}$$

where:

• i_c is the control current flowing into the control current pin C.

• R_in is the input resistance for the current control current value, i_c.

• i_c0 is the reference control current, that is, the control current at which input resistance is quoted on the datasheet.

• R_in0 is the input resistance measured at the reference control current i_c0.

Therefore, increasing control current reduces input resistance.

Limits

Because of the physical construction of an operational transconductance amplifier based on current mirrors, the transconductance current i_gm cannot exceed the control current. Hence the value of i_gm is limited by:

–ic ≤ igm ≤ ic

(1)

The output voltage is also limited by the supply voltage:

Vmin ≤ vo ≤ Vmax

(2)

where V_min is the Minimum output voltage, and V_max is the Maximum output voltage. Output voltage limiting is implemented by adding a low resistance to the output when the voltage limit is exceeded. The value of this resistance is set by the Additional output resistance at voltage swing limits parameter.

The transconductance current is also slew-rate limited, a value for slew rate limiting typically being given on datasheets:

$$-\mu \le \frac{d{i}_{gm}}{dt}\le \mu$$

where μ is the Maximum current slew rate.

Examples

Low-Pass Filter Using Operational Transconductance Amplifiers

Model a second-order active low-pass filter. The filter is characterized by the transfer function H(s) = 1 / ( (s/w1)^2 + (1/Q)*(s/w1) + 1 ) where w1 = 2*pi*f1, f1 is the cut-off frequency and Q is the quality factor. Double-click on the Set Design Parameters block to set parameters f1 and Q. The block mask calls a function which sets the parameter values in the model workspace.

• Open Model

Ports

Conserving

+ — Non-inverting input

electrical

Electrical conserving port associated with the op-amp non-inverting input.

- — Negative voltage

electrical

Electrical conserving port associated with the op-amp inverting input.

C — Control current

electrical

Electrical conserving port associated with the op-amp control current.

OUT — Output current

electrical

Electrical conserving port associated with the op-amp output. The port name is hidden on the block icon, but you can see it in simulation data logs.

Parameters

Nominal Measurements

Transconductance — Transconductance

9600 uS (default)

The transconductance, g_m, when the control current is equal to the Reference control current. This is the ratio of the transconductance current, i_gm, to the voltage difference, v, across the + and - pins.

Input resistance — Input resistance

25 kOhm (default)

The input resistance, R_in, when the control current is equal to the Reference control current. The input resistance is the ratio of the voltage difference, v, across the + and - pins to the current flowing from the + to the - pin.

Output resistance — Output resistance

3 MOhm (default)

The output resistance, R_out, when the control current is equal to the Reference control current. See above for the equation defining output resistance.

Reference control current — Reference control current

500 uA (default)

The control current at which the Transconductance, Input resistance, and Output resistance are quoted.

Dynamics

Dynamics — Dynamics

No lag (default) | Finite bandwidth with slew rate limiting

Select one of the following options:

• No lag — Do not model the dynamics of the relationship between output current and input voltage. This is the default.

• Finite bandwidth with slew rate limiting — Model the dynamics of the relationship between output current and input voltage using a first-order lag. If you select this option, the Bandwidth, Maximum current slew rate, and Initial current parameters appear on the Dynamics tab.

Bandwidth — Bandwidth of the first-order lag

2 MHz (default)

The bandwidth of the first-order lag used to model the dynamics of the relationship between output current and input voltage.

Dependencies

This parameter is visible only when the Dynamics parameter is set to Finite bandwidth with slew rate limiting.

Maximum current slew rate — Maximum rate-of-charge of transconductance current

2 A/us (default)

The maximum rate-of-change of transconductance current when there is no feedback around the device. Note that datasheets sometimes quote slew rate as a maximum rate of change of voltage. In this case, the value depends on the particular test circuit. To get an accurate value for Maximum current slew rate, reproduce the test circuit in a Simscape™ Electrical™ model, and tune the parameter value to match the datasheet value. If the test circuit is open-loop, and the load resistance is quoted, you can obtain an approximate value for the Maximum current slew rate by dividing the voltage slew rate by the load resistance.

Dependencies

This parameter is visible only when the Dynamics parameter is set to Finite bandwidth with slew rate limiting.

Initial current — Initial transconductance current

0 A (default)

The initial transconductance current (note, not the initial output current). This is the transconductance current sinking to both the internal output resistance, R_out, and the output pin.

Dependencies

This parameter is visible only when the Dynamics parameter is set to Finite bandwidth with slew rate limiting.

Limits

Minimum output voltage — Minimum output voltage

-15 V (default)

The output voltage is limited to be greater than the value of this parameter.

Maximum output voltage — Maximum output voltage

15 V (default)

The output voltage is limited to be less than the value of this parameter.

Additional output resistance at voltage swing limits — Additional output resistance at voltage swing limits

1 Ohm (default)

To limit the output voltage swing, an additional output resistance is applied between output and the power rail when the output voltage exceeds the limit. The value of this resistance should be low compared to the output resistance and circuit load resistance.

Minimum control current for simulation — Minimum control current for simulation

0.001 uA (default)

The control current measured at the control current pin C is limited to be greater than the value of this parameter. This prevents a potential divide-by-zero when calculating input and output resistance values based on the value of the control current.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2011b