Lab guide
Common-emitter gain: how good is the −RC/RE estimate?
2N3904 common-emitter and common-collector PSpice results against the quick estimate and the full formula, plus a check of a gain −10 design.
The gain of a common-emitter amplifier with an emitter resistor is usually estimated as Av ≈ −(RC‖RL)/RE. Here is how well that holds against PSpice, and what it leaves out.
1. Common emitter: gain versus load
VCC = 12 V, R1 = 620 kΩ, R2 = 180 kΩ, RC = 4.7 kΩ, RE = 470 Ω, a 500 Ω source resistance and a 1 Vp-p input. The operating point is ICQ = 1.41 mA, VCEQ = 4.69 V, with β = 165 and rπ = 3.08 kΩ.
| RL | RC‖RL | Estimate −(RC‖RL)/RE | With rπ | PSpice vo/vs |
|---|---|---|---|---|
| 2 kΩ | 1.4 kΩ | −2.99 | −2.83 | −2.80 |
| 3.3 kΩ | 1.94 kΩ | −4.12 | −3.91 | −3.87 |
| 4.7 kΩ | 2.35 kΩ | −5.00 | −4.73 | −4.68 |
| 5.6 kΩ | 2.56 kΩ | −5.44 | −5.15 | −5.09 |
- The estimate is about 7% high: it leaves rπ out of the denominator and ignores the signal lost in the source and bias resistors.
- The formula with rπ is within 1.1%: Av = −β(RC‖RL) / (rπ + (β+1)RE), multiplied by the input divider Rin/(Rin+Rs).
- A larger RL gives more gain: the collector sees RC‖RL, so connecting a load lowers the gain. The output is inverted (180°).
As a check, gm = IC/VT ≈ 54.5 mA/V, almost exactly PSpice's 53.6 mA/V.
2. Common collector (emitter follower)
With R1 = 180 kΩ, R2 = 470 kΩ and RE = 1.5 kΩ, a 6 Vp-p input gave 5.928 Vp-p out, a gain of 0.988, in phase. (β+1)RE / (rπ + (β+1)RE) with the source divider included gives 0.989, nearly the same. The gain is just under 1, but the high input and low output resistance make it a voltage buffer.
3. Checking a gain −10 design
On VCC = 15 V the design set RE = VE/IC and RC = 10·RE, then used standard values RC = 4.3 kΩ, RE = 430 Ω, R1 = 680 kΩ and R2 = 180 kΩ.
| Item | Target | PSpice |
|---|---|---|
| Voltage gain | −10 | −9.515 |
| ICQ | 1.7 mA | 1.8 mA |
| VCEQ | 6.5 V | 6.48 V |
The operating point landed close to the target, while the gain came out at −9.515, 5% short. Including rπ predicts −9.62, which accounts for most of the gap. Hitting −10 exactly needs RC = 10·(rπ + (β+1)RE)/β ≈ 4.47 kΩ.
| RC | Type | Predicted gain | Off target |
|---|---|---|---|
| 4.3 kΩ | E24 | −9.62 | −3.8% |
| 4.7 kΩ | E24 | −10.51 | +5.1% |
| 4.42 kΩ | E96 | −9.88 | −1.2% |
| 4.48 kΩ | 4.3 kΩ + 180 Ω in series | −10.02 | +0.2% |
In E24 the target falls between 4.3 kΩ and 4.7 kΩ, and the 4.3 kΩ chosen is the closer one. To get nearer, use 4.42 kΩ from E96 or 4.3 kΩ + 180 Ω in series. A larger RC lowers VCEQ by the added resistance × ICQ, about 0.32 V for an extra 180 Ω, so check that too.
4. In your lab report
- Take the gain as the ratio of output to input peak-to-peak voltages and note the phase. In decibels it is 20·log10|Av|.
- If the estimate and your measurement disagree, redo it with rπ included. Whatever difference remains is your real measurement error.
Convert gains to dB with the dB converter, compare measured and theoretical gains in a table with the lab data analyzer (free form), and see the BJT biasing guide for setting the operating point.