FET as Voltmeter - Lab Manual

FET as Voltmeter

1. Aim

To study the Field Effect Transistor (FET) as a voltmeter and investigate its characteristics as a high-impedance voltage measuring device.

2. Apparatus Used

Field Effect Transistor (JFET or MOSFET)
Regulated DC power supply (±15V)
Digital multimeter
Resistors: 1MΩ, 10kΩ, 100kΩ (as per circuit requirements)
Potentiometer (10kΩ)
Connecting wires
Breadboard
Microammeter or Milliammeter
Standard voltmeter (for reference measurements)

3. Circuit Diagram

Figure 1: Circuit diagram of FET configured as a voltmeter

4. Theory

A Field Effect Transistor (FET) can be configured as a high-impedance voltmeter due to its inherent high input impedance characteristics. This makes it particularly suitable for measuring voltages in circuits where conventional voltmeters might load the circuit and alter the measurement.

The principle of operation is based on the fact that in a FET, the gate-to-source voltage (V_GS) controls the drain current (I_D). When configured as a source follower (common drain configuration), the FET acts as a voltage buffer with the following characteristics:

Very high input impedance (typically 10⁹ to 10¹² Ω)
Low output impedance
Voltage gain slightly less than unity

In this configuration, the source voltage closely follows the gate voltage, with the relationship:

$V_S \approx V_G - V_{GS(th)}$

where V_S is the source voltage, V_G is the gate voltage (the voltage being measured), and V_GS(th) is the gate-to-source threshold voltage.

By measuring the drain current or the source voltage and applying appropriate calibration, we can determine the unknown input voltage at the gate with minimal loading of the circuit under test.

5. Formula

The basic formulas relevant to the FET voltmeter operation are:

1. Drain Current equation for FET in saturation region:

$I_D = I_{DSS}(1 - \frac{V_{GS}}{V_P})^2$

Where:

$I_D$ = Drain current
$I_{DSS}$ = Drain-to-source saturation current (at $V_{GS} = 0$)
$V_{GS}$ = Gate-to-source voltage
$V_P$ = Pinch-off voltage

2. For source follower configuration:

$V_{out} \approx V_{in} - V_{GS(th)}$

Where:

$V_{out}$ = Output voltage (measured at source)
$V_{in}$ = Input voltage (applied at gate)
$V_{GS(th)}$ = Gate-to-source threshold voltage

3. Voltage gain of the FET voltmeter:

$A_v = \frac{g_m R_S}{1 + g_m R_S}$

Where:

$A_v$ = Voltage gain
$g_m$ = Transconductance of the FET
$R_S$ = Source resistance

4. Calibration formula for FET voltmeter:

$V_{actual} = K \times I_D + C$

Where:

$V_{actual}$ = Actual input voltage
$I_D$ = Measured drain current
$K$ and $C$ = Calibration constants

6. Procedure

Set up the circuit as shown in the circuit diagram. Ensure all connections are correct.
Turn on the DC power supply and set it to ±15V (or as specified for your FET).
Before connecting the FET, verify the supply voltages with a standard voltmeter.
With no input voltage applied to the gate (or grounded gate), measure and record the initial drain current (I_D0).
Apply a known DC voltage (V_in) to the gate of the FET using the potentiometer.
Measure the corresponding drain current (I_D) or the voltage across the source resistor.
Vary the input voltage in steps (e.g., 0.5V or 1V increments) from 0V to 10V and record the corresponding drain current or source voltage readings.
Calculate the voltage gain of the circuit by comparing the output voltage (at source) with the input voltage (at gate).
Plot a graph of drain current (I_D) versus gate voltage (V_G).
Derive the calibration formula for the FET voltmeter based on the graph.
Test the FET voltmeter on unknown voltage sources and compare readings with a standard voltmeter.
Calculate the input impedance of the FET voltmeter circuit.
Turn off all equipment and disconnect the circuit after completing the measurements.

7. Observation Table

S. No.	Input Voltage V_in (V)	Drain Current I_D (mA)	Source Voltage V_S (V)	Voltage Gain A_v = V_S/V_in
1
2
3
4
5
6
7
8

S. No.	Unknown Voltage Source	Standard Voltmeter Reading (V)	FET Voltmeter Reading (V)	Percentage Error (%)
1
2
3

8. Calculations

Calculation of voltage gain:

$A_v = \frac{V_S}{V_{in}}$

Sample calculation:

If V_in = 5V and V_S = 4.8V, then:

$A_v = \frac{4.8V}{5V} = 0.96$
Calculation of the calibration formula:

From the graph of I_D versus V_G, determine the relationship in the form:

$V_G = m \times I_D + c$

Where m is the slope and c is the y-intercept of the calibration line.
Calculation of percentage error:

$\text{Percentage Error} = \frac{|V_{standard} - V_{FET}|}{V_{standard}} \times 100\%$
Calculation of input impedance:

The input impedance can be estimated by:

$Z_{in} = \frac{V_{in}}{I_{in}}$

Where I_in is the gate current, which is typically very small for a FET (in the nanoampere range).

9. Result

The FET voltmeter was successfully constructed and calibrated.
The voltage gain of the FET voltmeter was found to be approximately ______ (fill after experiment).
The calibration equation relating input voltage to drain current was determined to be: V_G = ______ × I_D + ______ (fill after experiment).
The average percentage error in measurements compared to the standard voltmeter was found to be ______% (fill after experiment).
The input impedance of the FET voltmeter was measured/calculated to be approximately ______ MΩ (fill after experiment).
The FET demonstrated excellent performance as a high-impedance voltmeter, making it suitable for measuring voltages in high-impedance circuits without significant loading effects.

10. Precautions

Handle the FET with care to avoid damage from static electricity. Use anti-static precautions when possible.
Ensure all connections are correct before powering on the circuit.
Verify the polarity of the power supply to avoid reverse biasing the FET inappropriately.
Keep the input voltage within the specified range to avoid damaging the FET.
Ensure the drain current does not exceed the maximum rated value for the FET being used.
Use shielded cables for connections to minimize noise and interference.
Allow the circuit to stabilize before taking readings to ensure accuracy.
Avoid touching the circuit components while measurements are being taken.
Ensure proper grounding of the circuit to avoid floating potentials.
Calibrate the FET voltmeter with a standard voltmeter before using it for measurements.
Turn off the power supply when making changes to the circuit.

11. Viva Voice Questions

Q: What is the main advantage of using a FET-based voltmeter over a conventional voltmeter?
A: The main advantage is the extremely high input impedance of the FET, which results in minimal loading of the circuit being measured. This makes it ideal for measuring voltages in high-impedance circuits where conventional voltmeters might significantly affect the measurement.
Q: Why is the source follower configuration preferred for a FET voltmeter?
A: The source follower (common drain) configuration is preferred because it provides a voltage gain close to unity, very high input impedance, and low output impedance, making it an ideal voltage buffer.
Q: How does temperature affect the performance of a FET voltmeter?
A: Temperature changes can affect the FET parameters, particularly the threshold voltage and transconductance, leading to drift in measurements. This is why calibration and temperature compensation may be necessary for precise measurements.
Q: Compare JFET and MOSFET for use in voltmeter applications.
A: JFETs typically have lower noise and are simpler to use, while MOSFETs can achieve even higher input impedance but are more susceptible to static damage. Both can be effective, with the choice depending on specific requirements such as input impedance, stability, and operating conditions.
Q: What causes the non-linearity in the FET voltmeter response?
A: Non-linearity is primarily due to the square-law relationship between gate voltage and drain current in a FET operating in the saturation region. Other factors include temperature effects, variations in FET parameters, and circuit non-idealities.
Q: Why is the voltage gain of a source follower slightly less than unity?
A: The voltage gain is less than unity due to the body effect and the voltage division between the FET's internal resistance (1/gm) and the external source resistance. Typically, the gain is around 0.9 to 0.98.
Q: How would you modify the FET voltmeter circuit to extend its measurement range?
A: The measurement range can be extended by using a voltage divider at the input or by employing multiple ranges with switchable resistors. Additionally, cascaded stages can be used for amplification of very small signals.
Q: What are the limitations of a FET voltmeter?
A: Limitations include temperature sensitivity, need for calibration, limited frequency response, potential drift over time, and susceptibility to noise and interference in certain environments.
Q: How does the gate leakage current affect the accuracy of the FET voltmeter?
A: Gate leakage current, though typically very small, can cause a voltage drop across high-impedance sources, affecting measurement accuracy. This is particularly relevant when measuring extremely high-impedance circuits or very low voltages.
Q: Explain the importance of biasing in the FET voltmeter circuit.
A: Proper biasing ensures the FET operates in the desired region (typically saturation) for optimal performance. It sets the operating point to provide maximum linearity, stability, and measurement range while preventing distortion.

For More experiment Manual Click on Link...