Library / Circuits, electronics and noise / ELN-25
Circuits, electronics and noise
Source-follower voltage gain
Midband gate-to-source voltage gain of a MOSFET source follower, where R is the total AC resistance from source to ground, with the load in parallel.
- Ref
- ELN-25
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Av [V/V]
A source follower (common drain) has a gate-to-source gain of gm R/(1 + gm R), where R is the total AC resistance from source to ground including the load in parallel. The gain is always less than one, and approaches 1 as gm R becomes large. The output resistance is about 1/gm, so the stage buffers a high-impedance signal to drive a low impedance.
Midband gate-to-source voltage gain of a MOSFET source follower, where R is the total AC resistance from source to ground, with the load in parallel. It is always below 1.
Calculator
- Loop gain, gm R4
- Output resistance, about 1/gm250 Ω
- Gain loss, 1 − Av0.2
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With gm R = 4 the follower passes 80 % of the input voltage to the output, losing 20 %.
- Its output resistance of about 250 Ω is why it can drive loads that would overwhelm a high-impedance source.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V/V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| gm Transconductance | 1e-4 to 0.1 S | 0.09091 | 0.9901 | 0.8992 | +10% | +1.85 % |
| R Source resistance in parallel with the load | 100 to 100,000 Ω | 0.2857 | 0.9975 | 0.7118 | +10% | +1.85 % |
Sweep of Source resistance in parallel with the load
| Source resistance in parallel with the load (Ω) | Voltage gain (V/V) |
|---|---|
| 100 | 0.2857 |
| 237.1 | 0.4868 |
| 562.3 | 0.6922 |
| 1,334 | 0.8421 |
| 3,162 | 0.9267 |
| 7,499 | 0.9677 |
| 17,780 | 0.9861 |
| 42,170 | 0.9941 |
| 100,000 | 0.9975 |
Sweep one variable
Variables and how each one contributes
Voltage gain
What the equation gives you. Everything else feeds it.
Transconductance
The transconductance, in S. A larger gm brings the gain closer to 1. Raising it by 10 % (to 0.0044) moves the result by +1.85 %, from 0.8 to 0.8148 V/V.
Source resistance in parallel with the load
The total resistance from source to ground (the load in parallel with the source resistor), in Ω. A larger R brings the gain closer to 1. Raising it by 10 % (to 1,100) moves the result by +1.85 %, from 0.8 to 0.8148 V/V.
Worked example with the values above
- Loop gain: gm R = 0.004 × 1,000 = 4.
- Denominator: 1 + gm R = 5.
- Av = 4 / 5 = 0.8.
Assumptions and limits
- A long-channel NMOS device in strong inversion and the square-law model.
- Triode and saturation formulas used only in their stated regions, and body effect ignored.
Common mistakes
- Using the triode formula when Vds is above Vgs − Vth, or the saturation formula when it is below.
- Forgetting that k here has no factor of one half in the triode formula.
- Applying the saturation gm formula to a device in weak inversion or velocity saturation.
Statistics and uncertainty
Real transistors depart from the square-law model, especially at short channel lengths, where velocity saturation changes the current dependence. The threshold voltage varies from part to part, so results with small overdrive are very sensitive to it.
Where it is used
- Bias and gain estimates for MOSFET amplifiers, switches and current sources.
- Quick checks of simulation results by hand.
Maths you need
- MOSFET regions: cut-off, triode and saturation
- Overdrive voltage: Vov = Vgs − Vth
- Small-signal model: gm and ro at a bias point