---
title: "Short note: Microwave mixer"
subject: "RF and Microwave Engineering"
chapter: 6
key: "semester_7/rf_and_microwave_engineering:mixer-note"
source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/mixer-note
site: BCT Engineering
---

# Short note: Microwave mixer

RF and Microwave Engineering · Chapter 6: RF Design Practices

- Asked in: 2072 Magh, 5 marks; 2070 Bhadra, 5 marks (asked 2 times)
- Video: [How a mixer in an RF receiver works](https://www.youtube.com/watch?v=6dFdwGNEemU) — Things You May Have Missed In Engineering Classes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/mixer-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-6

## Question

Write a short note on microwave mixer (mixer theory).

## Short answer

A microwave mixer uses a nonlinear device (e.g., Schottky diode) to produce sum and difference frequencies; the IF |f_RF - f_LO| is extracted. Conversion loss is 4–7 dB, image frequency is 2f_LO - f_RF. Balanced and double-balanced configurations improve isolation and reject LO noise.

## Answer

A **microwave mixer** is a three-port **frequency converter**. It combines an RF signal (f_RF) with a local-oscillator signal (f_LO) in a **non-linear device** to produce sum and difference frequencies. Usually the difference, the intermediate frequency (IF), is kept: f_IF = |f_RF − f_LO|.

**Mixer theory**

The device (usually a Schottky diode, or a FET) has a non-linear I–V curve:

```text
i = a0 + a1·v + a2·v² + a3·v³ + ...
v = Vr cos ωr t + VL cos ωL t
a2·v² term gives:
 a2·Vr·VL·[cos(ωr − ωL)t + cos(ωr + ωL)t]
=> IF at |fr − fL|, also fr + fL,
   harmonics and intermod products
```

A filter at the output selects the IF. The IF amplitude is proportional to V_r, so the modulation of the RF signal is kept.

```text
 RF (fr) --->[        ]---> IF = |fr − fL|
             [ MIXER  ]  (+ filter)
 LO (fL) --->[        ]
```

**Important terms**
- **Conversion loss:** L_c = 10 log(P_RF / P_IF), typically 4–7 dB for diode mixers.
- **Image frequency:** f_im = 2f_LO − f_RF, the mirror image of f_RF on the other side of f_LO (f_IF away from f_LO). It also gives the same IF, so it must be filtered out before the mixer.
- **Noise figure:** about equal to the conversion loss for a diode mixer (SSB).
- **Isolation** between the LO, RF and IF ports.

**Types**
- **Single-ended:** one diode. Simple, but with poor isolation and no LO noise rejection.
- **Balanced:** two diodes with a 90° or 180° hybrid. Cancels LO AM noise and some spurs, and gives better RF–LO isolation.
- **Double-balanced:** four diodes (ring) with baluns. Best isolation, rejects even harmonics, wide bandwidth.
- **Image-reject:** two mixers with quadrature hybrids to cancel the image.

**Applications:** down-conversion in superheterodyne receivers, up-conversion in transmitters, phase detectors and modulators.

## Check yourself

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

1. Why can a mixer produce the IF?
   A. It uses a linear device
   B. A non-linear device (diode or FET) with a square-law term produces sum and difference frequencies
   C. A resonant filter alone creates new frequencies
   D. The LO is amplified to the IF
   Answer: B. The a2 v^2 term gives products at fr - fL and fr + fL. A filter then selects the IF = |fr - fL|. (Key point: Principle of mixing)

2. What is the image frequency and why must it be filtered?
   A. The second harmonic of the LO; it damages the diode
   B. The frequency on the other side of fLO that gives the same IF, so it must be filtered before the mixer
   C. The IF itself
   D. The sum frequency fr + fL
   Answer: B. Both fLO + fIF and fLO - fIF produce the same IF, so the unwanted one must be rejected before mixing. (Key point: Image frequency)

3. How is conversion loss defined and what is the typical value for diode mixers?
   A. 10 log(P_IF/P_RF); 40 dB
   B. 10 log(P_RF/P_IF); 4-7 dB
   C. 10 log(P_LO/P_RF); 20 dB
   D. 10 log(P_RF/P_LO); 1 dB
   Answer: B. It is the ratio of RF input power to IF output power, typically 4-7 dB for diode mixers, and it roughly equals the noise figure. (Key point: Conversion loss)

4. Which mixer gives the best isolation and rejects even harmonics?
   A. Single-ended
   B. Single balanced with 90° hybrid
   C. Double-balanced (diode ring with baluns)
   D. Image-reject
   Answer: C. The four-diode ring with baluns gives the best port isolation and wide bandwidth, and rejects even harmonics. (Key point: Mixer types)