---
title: "Tuned amplifier applications, bandwidth, Q factor"
subject: "Electronics Devices and Circuit"
chapter: 4
key: "semester_3/electronics_devices_and_circuit:tuned-amplifier-applications-resonance-q"
source: https://www.bctengineer.com/q/semester_3/electronics_devices_and_circuit/tuned-amplifier-applications-resonance-q
site: BCT Engineering
---

# Tuned amplifier applications, bandwidth, Q factor

Electronics Devices and Circuit · Chapter 4: Output Stages and Power Amplifiers

- Asked in: 2080 Baisakh, 2+6 marks
- Video: [Single Tuned Amplifier - Capacitance Coupled Single Tuned Amplifier](https://www.youtube.com/watch?v=Ndk7WBKi73U) — Padmasri Naban
- 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/tuned-amplifier-applications-resonance-q
- Whole chapter: https://www.bctengineer.com/md/semester_3/electronics_devices_and_circuit/chapter-4

## Question

What are the applications of tuned amplifiers? Determine its 3 dB Bandwidth, Resonance frequency and Quality factor.

## Short answer

Used in RF/IF amplifiers, transmitters, and narrow‑band systems. Resonance frequency fr = 1/(2π√(LC)); quality factor Q = ωr L/r; 3 dB bandwidth BW = fr/Q. The tank’s loaded Q determines selectivity, and gain peaks at fr.

## Answer

#### Applications of tuned amplifiers
- RF amplifiers at the front end of radio and TV receivers (select one station and reject others).
- IF amplifiers in superheterodyne receivers (for example 455 kHz in AM, 10.7 MHz in FM).
- Transmitters: tuned power amplifiers and frequency multipliers.
- Communication systems where a narrow band must be amplified: wireless links, radar, telemetry.
- Band-pass filtering together with amplification.

#### Resonance frequency, Q and 3 dB bandwidth
A tuned amplifier uses a parallel LC tank (coil inductance L with series resistance r, and capacitor C) as the collector or drain load.

**Resonance frequency:**

fr = 1 / (2π √(LC))  (for Q > 10)

At resonance the tank impedance is purely resistive and maximum: Zr = Rp = L/(C r) = Q ωr L.

**Quality factor:**

Q = ωr L / r = Rp/(ωr L)

When the transistor output resistance and the load are in parallel with the tank, Rp is replaced by the total effective resistance Reff, giving the loaded Q:  QL = Reff/(ωr L).

**3 dB bandwidth:**

BW = f2 − f1 = fr/Q

where f1 and f2 are the frequencies at which the gain falls to 0.707 of the maximum:

f1 ≈ fr − BW/2,  f2 ≈ fr + BW/2

**Voltage gain at resonance:** Av = −gm Reff (maximum). At other frequencies, Av = −gm Reff / (1 + j Q (f/fr − fr/f)) ≈ −gm Reff / (1 + j 2Q δ), with δ = (f − fr)/fr.

#### Example
L = 100 µH, C = 253 pF, loaded Q = 50:

fr = 1/(2π√(100×10⁻⁶ × 253×10⁻¹²)) = 1.0 MHz, BW = 1 MHz/50 = 20 kHz, so f1 = 990 kHz and f2 = 1010 kHz.

A higher Q gives a narrower band and better selectivity.

## Check yourself

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

1. What is the resonance frequency of the parallel LC tank load?
   A. fr = 2π sqrt(LC)
   B. fr = 1/(2π LC)
   C. fr = 1/(2π sqrt(LC))
   D. fr = sqrt(LC)/(2π)
   Answer: C. At resonance XL = XC, giving fr = 1/(2π sqrt(LC)). (Key point: Resonance frequency)

2. How is the 3 dB bandwidth related to Q?
   A. BW = fr x Q
   B. BW = fr/Q
   C. BW = Q/fr
   D. BW = fr/Q^2
   Answer: B. BW = f2 - f1 = fr/Q, so a higher Q gives a narrower band and better selectivity. (Key point: Bandwidth)

3. For fr = 1 MHz and loaded Q = 50, what are the 3 dB bandwidth and band edges?
   A. 20 kHz; 990 kHz and 1010 kHz
   B. 50 kHz; 975 kHz and 1025 kHz
   C. 20 kHz; 980 kHz and 1020 kHz
   D. 2 kHz; 999 kHz and 1001 kHz
   Answer: A. BW = 1 MHz/50 = 20 kHz, and f1,2 = fr -/+ BW/2 = 990 kHz and 1010 kHz. (Key point: Numerical example)

## Related in Electronics Devices and Circuit

- [Class A tuned amplifier frequency range](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Atuned-amplifier-3db-bandwidth) — Electronics Devices and Circuit, chapter 4, asked 16×
- [Synchronous vs stagger tuned amplifier](https://www.bctengineer.com/question.md?key=semester_3%2Felectronics_devices_and_circuit%3Asynchronous-vs-stagger-tuned) — Electronics Devices and Circuit, chapter 4

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