Short note: Microwave mixer

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:

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.

 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.