---
title: "Bypass capacitor significance; CE small signal analysis"
subject: "Electronics Devices and Circuit"
chapter: 2
key: "semester_3/electronics_devices_and_circuit:ce-bypass-capacitor-small-signal"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/ce-bypass-capacitor-small-signal
site: BCT Engineering
---

# Bypass capacitor significance; CE small signal analysis

Electronics Devices and Circuit · Chapter 2: The Bipolar Junction Transistor

- Asked in: 2079 Bhadra, 2+6 marks; 2073 Chaitra, 2+6 marks (asked 2 times)
- Video: [CE Amplifier (with bypass capacitor) AC analysis || Small signal model](https://www.youtube.com/watch?v=8Ig3ZqAeUm4) — The Mid Programmer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/ce-bypass-capacitor-small-signal
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-2

## Question

What is the significance of bypass capacitor in CE amplifier? Draw the small signal model of voltage divider bias for emitter bypassed capacitor CE amplifier circuit and find its input impedance, output impedance and voltage gain.

## Short answer

Bypass capacitor CE shorts RE at signal frequencies, removing AC negative feedback to raise gain. Small-signal model: R1||R2||rπ at input, current source gm vπ at output. Zin = R1||R2||rπ, Zo ≈ RC, Av = –gm(RC||RL).

## Answer

#### Significance of the bypass capacitor
The bypass capacitor CE is connected across the emitter resistor RE. At dc it is open, so RE gives bias stability (negative feedback). At signal frequencies its reactance is very small, so it **shorts RE to ground for ac**. This removes the ac negative feedback, so the voltage gain is large (Av = -gm RC) instead of being reduced to -RC/RE. It also needs to be large: XC ≪ re at the lowest signal frequency.

#### Small-signal model (hybrid-π) of divider-bias CE amplifier with CE
```text
 vs--Rs--+--B--rπ--E(gnd)      C
         |      |   \         |
       R1||R2   vπ   (gm vπ)--+--RC||RL--GND
         |
        GND
```
- Input side: R1 || R2 in parallel with rπ between base and ground (emitter grounded by CE).
- Output side: current source gm vπ in parallel with ro, RC and RL.

With rπ = β/gm = β VT/IC and gm = IC/VT.

#### Input impedance
```text
Zin = R1 || R2 || rπ
```

#### Output impedance
Set vs = 0, so vπ = 0 and the source gm vπ = 0:
```text
Zo = RC || ro  ≈ RC     (looking into the collector, load excluded)
```

#### Voltage gain
```text
vo = -gm vπ (RC || RL || ro) ,   vπ = vin

Av = vo/vin = -gm (RC || RL)
```
For example, IC = 1.5 mA gives gm = 60 mA/V; with RC||RL = 4 kΩ, Av = -240. The negative sign shows a 180° phase shift.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does the bypass capacitor do?
   A. Opens RE at ac
   B. Blocks dc at the input
   C. Reduces bias stability
   D. Shorts RE for ac, removing negative feedback and raising gain
   Answer: D. At dc it is open so RE stabilises bias; at signal frequency it shorts RE. (Key point: Purpose)

2. What is Zin with bypass?
   A. R1||R2||(beta+1)RE
   B. RC
   C. r_pi + RC
   D. R1||R2||r_pi
   Answer: D. With the emitter grounded, r_pi is across the base. (Key point: Zin)

3. What is Av?
   A. 1
   B. -gm(RC||RL)
   C. -RC/RE
   D. beta
   Answer: B. vo = -gm v_pi (RC||RL), v_pi = vin. (Key point: Gain)

4. What is Zo?
   A. About RC
   B. About RE
   C. About infinity
   D. About r_pi
   Answer: A. With vs = 0, gm v_pi = 0, so Zo = RC||ro, about RC. (Key point: Zo)

## Related in Electronics Devices and Circuit

- [CE small-signal model, gain and input impedance](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-small-signal-gain-input-impedance) — Electronics Devices and Circuit, chapter 2
- [CE amplifier input, output resistance and gain (RE1, RE2)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-partial-bypass-numeric) — Electronics Devices and Circuit, chapter 2
- [Design divider-bias CE amplifier with gain -90](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-design-gain-minus-90) — Electronics Devices and Circuit, chapter 2
- [CC amplifier small-signal model, Rin and gain](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Acc-small-signal-rin-gain) — Electronics Devices and Circuit, chapter 2
- [Design CE amplifier (BC547B, no bypass)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-design-bc547b-no-bypass) — Electronics Devices and Circuit, chapter 2
- [Design divider-bias CE amplifier (24 V, 2 mA, beta 90)](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Ace-design-24v-2ma-beta90) — Electronics Devices and Circuit, chapter 2

## Related in other subjects

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