Match List I with List II List – I List – II JFET - Bias Characteristic Equation A. Self - bias I. \(\rm I_D = \frac{V_{SS}-V_{GS}}{R_S}\) B. Voltage – divider bias II. \(\rm I_D = \frac{V_{EE}-V_{BE}}{R_E}\) C. Source bias III. V GS = -I DR S D. Current – source bias IV. \(\rm I_D = \frac{V_{G}-V_{GS}}{R_S}\) Choose the correct answer from the options given below:
A ‐ III, B ‐ IV, C ‐ I, D ‐ II
Understanding JFET Bias Methods and Characteristic Equations
JFET biasing is essential to establish a stable DC operating point (Q-point) for the JFET amplifier. The Q-point determines the quiescent drain current (\(\rm I_D\)) and gate-source voltage (\(\rm V_{GS}\)) when no AC signal is applied. Different biasing methods are used to achieve this, and each method leads to a specific relationship between the circuit voltages, resistances, and the JFET parameters.
Let's analyze each JFET bias method listed and derive or identify its characteristic equation from the given options.
Analysis of JFET Bias Types and Equations
- A. Self-bias:
In a self-bias circuit, a resistor (\(\rm R_S\)) is connected between the source terminal and ground. The gate is typically connected to ground through a resistor (\(\rm R_G\)), which is very large and carries negligible current, making the gate voltage (\(\rm V_G\)) approximately 0V. The drain current (\(\rm I_D\)) flows through \(\rm R_S\), creating a voltage drop across it (\(\rm V_S = I_D R_S\)). The gate-source voltage (\(\rm V_{GS}\)) is given by \(\rm V_{GS} = V_G - V_S\). Since \(\rm V_G \approx 0\), we get \(\rm V_{GS} = 0 - I_D R_S = -I_D R_S\). This equation directly relates \(\rm V_{GS}\) and \(\rm I_D\) for a given \(\rm R_S\).
This matches with List II equation III: \(\rm V_{GS} = -I_D R_S\).
- B. Voltage-divider bias:
This method uses a voltage divider network (usually two resistors \(\rm R_1\) and \(\rm R_2\)) connected to the gate to establish a fixed gate voltage (\(\rm V_G = V_{DD} \frac{R_2}{R_1+R_2}\)). A source resistor (\(\rm R_S\)) is also used. The source voltage (\(\rm V_S\)) is related to the drain current by \(\rm V_S = I_D R_S\). The gate-source voltage is \(\rm V_{GS} = V_G - V_S = V_G - I_D R_S\). Rearranging this equation to express \(\rm I_D\) in terms of \(\rm V_G\), \(\rm V_{GS}\), and \(\rm R_S\): \(\rm I_D R_S = V_G - V_{GS}\), which gives \(\rm I_D = \frac{V_{G}-V_{GS}}{R_S}\). This equation represents the load line for the voltage-divider bias circuit on the \(\rm I_D\) vs \(\rm V_{GS}\) characteristic curve.
This matches with List II equation IV: \(\rm I_D = \frac{V_{G}-V_{GS}}{R_S}\).
- C. Source bias:
In a source bias circuit, the gate is usually grounded (\(\rm V_G = 0\)), and the source resistor (\(\rm R_S\)) is connected to a negative supply voltage (\(\rm -V_{SS}\)). The drain current (\(\rm I_D\)) flows through \(\rm R_S\). The voltage at the source terminal (\(\rm V_S\)) and the negative supply voltage \(\rm -V_{SS}\) relate to the voltage drop across \(\rm R_S\) by \(\rm V_S - (-V_{SS}) = I_D R_S\), or \(\rm V_S + V_{SS} = I_D R_S\). The gate-source voltage is \(\rm V_{GS} = V_G - V_S = 0 - V_S = -V_S\), so \(\rm V_S = -V_{GS}\). Substituting this into the previous equation: \(\rm -V_{GS} + V_{SS} = I_D R_S\). Rearranging to solve for \(\rm I_D\): \(\rm I_D R_S = V_{SS} - V_{GS}\), which gives \(\rm I_D = \frac{V_{SS}-V_{GS}}{R_S}\).
This matches with List II equation I: \(\rm I_D = \frac{V_{SS}-V_{GS}}{R_S}\).
- D. Current-source bias:
This biasing method uses a constant current source connected to the source terminal of the JFET. This current source is often implemented using a BJT or another JFET. If a BJT is used as the current source, its collector current (which is approximately equal to the emitter current \(\rm I_E\)) sets the JFET's drain current (\(\rm I_D \approx I_E\)). A common BJT current source configuration uses an emitter resistor \(\rm R_E\) connected to a negative supply voltage \(\rm V_{EE}\). The base is typically at a fixed voltage (e.g., grounded or biased by a voltage divider). Assuming the base is grounded (\(\rm V_B = 0\)) and the emitter is at voltage \(\rm V_E\), the voltage across \(\rm R_E\) is \(\rm V_E - V_{EE}\). The emitter current is \(\rm I_E = \frac{V_E - V_{EE}}{R_E}\). The base-emitter voltage is \(\rm V_{BE} = V_B - V_E = 0 - V_E = -V_E\), so \(\rm V_E = -V_{BE}\). Substituting this into the \(\rm I_E\) equation gives \(\rm I_E = \frac{-V_{BE} - V_{EE}}{R_E}\). However, List II equation II is \(\rm I_D = \frac{V_{EE}-V_{BE}}{R_E}\). This equation corresponds to a common BJT current source calculation where \(V_{BE}\) is treated as approximately constant (e.g., 0.7V for silicon) and the base voltage is fixed, often to ground, while \(\rm R_E\) is connected to the negative supply \(V_{EE}\). The voltage at the emitter will be \(\approx -V_{BE}\). Then \(\rm I_E = \frac{-V_{BE} - V_{EE}}{R_E} = \frac{-(V_{BE} + V_{EE})}{R_E}\). There seems to be a sign difference or convention issue in option II compared to the standard derivation from a BJT current source where \(V_{EE}\) is a negative value. However, interpreting \(\rm V_{EE}\) as the magnitude of the negative supply (so the supply is at \(-V_{EE}\)) and the base is at 0V, the emitter voltage is approximately \(-V_{BE}\) (relative to ground). The voltage across \(\rm R_E\) is \(-V_{BE} - (-V_{EE}) = V_{EE} - V_{BE}\). Thus, \(\rm I_E = \frac{V_{EE}-V_{BE}}{R_E}\). Since \(\rm I_D \approx I_E\), we get \(\rm I_D \approx \frac{V_{EE}-V_{BE}}{R_E}\).
This matches with List II equation II: \(\rm I_D = \frac{V_{EE}-V_{BE}}{R_E}\).
Summary of JFET Bias Matching
Based on the analysis:
- Self-bias (A) matches with \(\rm V_{GS} = -I_D R_S\) (III).
- Voltage-divider bias (B) matches with \(\rm I_D = \frac{V_{G}-V_{GS}}{R_S}\) (IV).
- Source bias (C) matches with \(\rm I_D = \frac{V_{SS}-V_{GS}}{R_S}\) (I).
- Current-source bias (D) matches with \(\rm I_D = \frac{V_{EE}-V_{BE}}{R_E}\) (II).
The correct matching is A - III, B - IV, C - I, D - II.
| List I (JFET Bias) | List II (Characteristic Equation) | Matching |
|---|---|---|
| A. Self - bias | I. \(\rm I_D = \frac{V_{SS}-V_{GS}}{R_S}\) | A ‐ III |
| B. Voltage – divider bias | II. \(\rm I_D = \frac{V_{EE}-V_{BE}}{R_E}\) | B ‐ IV |
| C. Source bias | III. \(\rm V_{GS} = -I_D R_S\) | C ‐ I |
| D. Current – source bias | IV. \(\rm I_D = \frac{V_{G}-V_{GS}}{R_S}\) | D ‐ II |
Revision Table: JFET Biasing Equations
Here is a quick review of the characteristic equations for these JFET bias types:
| JFET Bias Type | Characteristic Equation | Notes |
|---|---|---|
| Self-bias | \(\rm V_{GS} = -I_D R_S\) | Relates \(\rm V_{GS}\) and \(\rm I_D\). Gate voltage is typically 0V. |
| Voltage-divider bias | \(\rm I_D = \frac{V_{G}-V_{GS}}{R_S}\) | \(\rm V_G\) is fixed by the voltage divider. This is a load line equation. |
| Source bias | \(\rm I_D = \frac{V_{SS}-V_{GS}}{R_S}\) | Gate voltage is typically 0V. \(\rm -V_{SS}\) is the negative supply connected to \(\rm R_S\). |
| Current-source bias | \(\rm I_D \approx \frac{V_{EE}-V_{BE}}{R_E}\) | Assumes BJT current source implementation, where this is the BJT's emitter current equation. |
Additional Information: JFET Biasing Concepts
JFETs (Junction Field-Effect Transistors) require biasing to set the DC operating point within the pinch-off or saturation region (for common amplifier configurations). Proper biasing ensures that the transistor operates linearly for AC signals without distortion.
- Purpose of Biasing: To establish a stable Q-point (\(\rm I_D, V_{GS}\)) independent of transistor parameter variations and temperature changes.
- Shockley's Equation: This fundamental equation describes the relationship between drain current (\(\rm I_D\)) and gate-source voltage (\(\rm V_{GS}\)) for a JFET in the pinch-off region:
\(\rm I_D = I_{DSS}\left(1 - \frac{V_{GS}}{V_P}\right)^2\)
where \(\rm I_{DSS}\) is the drain current at \(\rm V_{GS}=0\) and \(\rm V_P\) is the pinch-off voltage (or \(\rm V_{GS(off)}\)). Biasing circuits provide a second equation (the load line) that, when solved simultaneously with Shockley's equation, determines the Q-point.
- Types of JFET Bias:
- Fixed Bias (requires a negative supply for \(\rm V_{GS}\))
- Self-bias (uses source resistor)
- Voltage-divider bias (uses voltage divider and source resistor)
- Source bias (uses source resistor connected to a negative supply)
- Current-source bias (uses an active current source)
Understanding the characteristic equation for each bias circuit is crucial for calculating the Q-point and analyzing the circuit's behavior.
Important Questions from Types of FET
A JFET has high input impedance because-
The transconductance g mof a JFET is equal to:
\(\frac{ I _{ DSS }}{ V _{ P }}\left(1-\frac{ V _{ GS }}{ V _{ P }}\right)\)
The CMOS inverter can be used as an amplifier when:
In JFET, the Pinch‐off Voltage can be defined as:
In JFET, the current density in the x-direction is:
A. σ(x)E x
B. qN DμE x
C. \(\rm \frac{q}{2 \in_s}N_D\mu\)
D. \(\rm \frac{N_D\mu}{2 \in_s}\)
Choose the correct answer from the options given below:
