MOSFET biasing: why voltage-divider bias is so sensitive to the threshold voltage

Working out the operating point of 2N7000 voltage-divider and self-bias circuits with the square law, and how far one resistor or a threshold spread moves it.

To use a MOSFET as an amplifier you park its operating point (I_DQ, V_DSQ) near the middle of the saturation region. The numbers here are calculated with V_th = 2.084 V and K = 147 mA/V², fitted to 2N7000 PSpice results in the MOSFET I–V guide. A real part can come out very differently depending on its V_th; section 7 compares them with what was measured on a breadboard.

1. Circuit and formulas

Saturation needs V_GS ≥ V_th and V_DS ≥ V_GS − V_th. An operating point near cut-off or the triode edge clips part of each half cycle, so an amplifier aims for the middle of saturation.

2. Voltage-divider bias: changing R₂

V_DD = 10 V, R₁ = 560 kΩ and R_D = 1 kΩ. With no R_S, V_GS = V_G.

Changing R₂ by only 12.5%, from 160 kΩ to 180 kΩ, takes I_D from 2.8 mA to 9.88 mA and into the triode region. V_G sits just 0.14 V above V_th, and the current goes with the square of that margin. It is the same problem as a BJT with a small V_TH − V_BE (BJT biasing guide).

3. Voltage-divider bias: changing R_D

R₂ stays at 160 kΩ and only R_D changes.

In saturation I_D depends on V_GS alone, so it stays put as R_D changes and only V_DS falls. Once V_DS drops below V_GS − V_th the device enters the triode region, which limits R_D to the value below. Above it, R_D itself chokes the current.

4. Self bias: adding a source resistor R_S

V_DD = 15 V, R₁ = 820 kΩ, R₂ = 330 kΩ and R_D = 2.2 kΩ. V_G = 4.304 V is well above threshold, but V_GS loses the source voltage I_D·R_S. Solving the two equations together gives a quadratic whose positive root is the operating point.

• A small R_S means triode: at 180 Ω and 300 Ω plenty of V_GS is left, the device tries to pass a large current, nearly all of V_DD drops across R_D and V_DS ends up near 0.
• From 1 kΩ it saturates: V_GS comes down close to threshold and the current limits itself. More current raises V_S, which cuts V_GS: negative feedback.

5. When the threshold differs from part to part

The 2N7000 datasheet spreads V_th from 0.8 to 3.0 V. Holding K and moving V_th by ±0.2 V shows the difference between the two circuits clearly.

Voltage-divider bias goes into the triode region if V_th is just 0.2 V lower and cuts off if it is 0.2 V higher. Self bias only moves I_D between 1.91 mA and 2.3 mA over the same range. So a divider circuit that matched nicely in PSpice coming out in a completely different mode on the breadboard is nothing strange.

6. Design: choosing resistors for a target operating point

An example on V_DD = 12 V with R₂ = 150 kΩ, aiming for V_GSQ = 2.2 V, I_DQ = 3 mA and V_DSQ = 6.8 V. With no gate current, R₁ follows from the divider and R_D from KVL.

The nearest standard values are 680 kΩ and 1.8 kΩ. Making R₁ 1.8% larger, though, lowers V_G by 31 mV. A part that meets the target (V_GS 2.2 V giving 3 mA with V_th = 2.093 V) must have K = 262 mA/V², and with that part the numbers are:

Swapping one resistor for its standard value cut I_D to about 50% of the target. To set the point accurately with divider bias alone, add a trimmer in series with R₁, or more practically add a source resistor and turn it into self bias. In simulation these numbers change with the device model, so your own simulation not matching this table is not a sign of a mistake.

7. Results measured on a breadboard

The same circuits were built on a breadboard and read with a multimeter. Currents are recalculated from the recorded voltages as I_D = V_RD/R_D, and each mode is judged by V_DS ≥ V_GS − V_th with V_th ≈ 1.535 V from the I–V bench measurement. 'Bench-fit prediction' uses that lab's measured V_th and K (≈ 123 mA/V²) with nominal resistor values.

Voltage-divider bias, changing R₂ (R_D 1 kΩ)

Voltage-divider bias, changing R_D (R₂ 160 kΩ)

Self bias (R_D 2.2 kΩ)

• The previous lab's measured V_th predicts it: all four self-bias points matched the bench-fit prediction within 1.5%. The two small-R_S points are in triode, where R_D sets the current and any model agrees; at 1 kΩ and 2.2 kΩ, in saturation, the PSpice fit (V_th 2.084 V) comes out 19% and 19% below the bench. Nearly the whole gap is the threshold voltage.
• The divider runs almost entirely in triode: from R₂ = 150 kΩ, V_DS sticks below 0.1 V and I_D stops at V_DD/R_D ≈ 10 mA, within 0.2% of the bench-fit prediction. In the R_D table the current simply follows V_DD/R_D. Here R_D sets the current, not the MOSFET.
• Only the R₂ = 130 kΩ column misses: the prediction is 9.86 mA (triode), the bench gave 8.86 mA with V_DS 1.13 V, on the saturation side. For the measured V_GS of 1.85 V to give that current, V_th would be about 1.582 V, so a threshold just 47 mV different explains it. It shows how touchy a circuit running just above threshold is.
• The handout's V_th of 2.093 V gives the wrong call: at R₂ 130 kΩ, 150 kΩ, V_GS was 1.85 V, 2.08 V, below 2.093 V, so the part 'should' be cut off, yet mA-level currents flowed. Judge the mode with the V_th you measured on your own part, and say which value you used.
• Do the two current readings agree? In self bias, V_RD/R_D and V_S/R_S differ by at most 1.6%, which confirms both the zero gate current and the wiring.
• The gate sat lower than calculated: the R₁, R₂ divider gives V_G = 4.304 V, the bench read 4.135 V. The meter's 10 MΩ input alone pulls it to 4.205 V, and resistor tolerance can cover the rest. The bench-fit prediction used nominal values and still matched, which also shows self bias soaking up small differences like this.

8. Common measurement mistakes

• Touching the gate with the meter moves the operating point: the meter's input resistance (typically 10 MΩ) lands in parallel with R₂. In the divider circuit (R₁‖R₂ ≈ 124 kΩ) V_G falls by 27 mV and I_D goes from 2.8 mA to 1.8 mA. In the self-bias circuit (R_S 1 kΩ, R₁‖R₂ ≈ 235 kΩ) it only moves from 2.1 mA to 2 mA. Measure V_RD first, then watch whether it changes while the probe is on the gate.
• Judge the mode with your part's V_th: the handout's 2.093 V is the model's. Use the V_th from your I–V lab to test V_DS ≥ V_GS − V_th, and say in the report which value you used.
• Take I_D as V_RD/R_D: in the self-bias circuit also work out V_RS/R_S and compare. With no gate current they must match; if not, suspect the wiring or a resistor value.
• If the currents are several times off the calculation: it is almost always V_th. Solve √I_D = √K·(V_GS − V_th) backwards from your measured V_GS and I_D to get the part's V_th.

9. In your lab report

• Draw the DC load line (V_DD on the V_DS axis, V_DD/(R_D + R_S) on the I_D axis) and mark the operating points: R₂ slides the point along the line, while R_D and R_S change the line's slope.
• Add the boundary V_DS = V_GS − V_th (triode against saturation) to the same plot as the basis for each mode call.

Check the gate divider with the voltage divider calculator and resistor currents and power with the Ohm's law calculator. For the BJT equivalent, try the BJT bias calculator.