# Panyampur frékuénsi

Dina telekomunikasi, frequency mixer atawa panyampur frékuénsi nyaéta sirkuit atawa alat anu non liniér atawa robah-robah dumasar waktu (time-varying) anu narima dua asupan dina frékuénsi nu béda sarta ngahasilkeun hiji kaluaran mangrupa campuran sinyal dina sababaraha kamungkinan:

1. pajumlahan frékuénsi-frékuénsi sinyal-sinyal asupan
2. béda antara frékuénsi-frékuénsi sinyal-sinyal asupan
3. dua frékuénsi asli asupan — nu ieu mindeng dianggap parasit.

Éfék non liniér bisa dihasilkeun ku cara ngagunakeun hiji komponén listrik non liniér, saperti hiji dioda. Éfék parobahan dumasar waktu (time-varying) bisa dijieun ku cara maké hiji sirkuit kakalian (multiplier circuit) saperti Gilbert Cell atawa stop kontak pasif (passive switches).

Manipulasi frékuénsi nu dilakonan ku hiji panyampur bisa dipaké pikeun mindahkeun sinyal antara pita-pita frékuénsi atawa pikeun ngodekeun (to encode) sarta meupeuskeun kode (to decode) sinyal. Salah sahiji pamakéan lianna nyaéta sabagé product detector.

## Gambaran sacara matematis

The input signals are, in the simplest case, sinusoidal voltage waves, representable as

${\displaystyle v_{i}(t)=A_{i}\sin 2\pi f_{i}t\,}$

where éach A is an amplitude, éach f is a frequency, and t represents time. (In réality even such simple waves can have various phases, but that does not enter here.) One common approach for adding and subtracting the frequencies is to multiply the two signals; using the trigonometric identity

${\displaystyle \sin(A)\cdot \sin(B)\equiv {\frac {1}{2}}\left[\cos(A-B)-\cos(A+B)\right]}$

we have

${\displaystyle v_{1}(t)v_{2}(t)={\frac {A_{1}A_{2}}{2}}\left[\cos 2\pi (f_{1}-f_{2})t-\cos 2\pi (f_{1}+f_{2})t\right]}$

where the sum (${\displaystyle f_{1}+f_{2}}$) and difference (${\displaystyle f_{1}-f_{2}}$) frequencies appéar. This is the inverse of the production of acoustic beats.