# Dual and Single Sideband

Heterodyne receivers at sub-millimeter wavelengths commonly uses a mixer as the first stage. The mixer mixes the signal and the Local Oscillator (LO) to form a Intermediate Frequency (IF) which is amplified and analyzed. A particular IF frequency is generated by $\nu^{\,}_{IF}=\nu_{Signal}-\nu_{LO}$ or $\nu_{IF}=\nu_{LO}-\nu_{Signal}$. The first alternative generates the Upper SideBand (USB) and the second alternative the Lower SideBand (LSB).

If both the USB and LSB possibilities are present in the output from the mixer the system is a Dual Sideband (DSB) system. By inserting a filter before the mixer it is possible to attenuate the unwanted sideband to get a Single SideBand (SSB) system.

Balanced mixers can also separate the upper and lower sidebands – in Sideband Separating mixers both the USB and LSB are generated separately. A Sideband Separating mixer is denoted by 2SB.

As explained above in a DSB system both possibilities are present in the output. As an example if the receiver is tuned to $230.538$ GHz USB it will also see frequencies around $230.538$ GHz $-^{\,}2\cdot\nu_{IF}$. At the JCMT the 230 GHz band receiver has an IF frequency of 4 GHz. In the above example the receiver will see frequencies around 230.538 GHz and 222.538 GHz.

Even with a SSB receiver there is some leakage – the unwanted sideband is typically attenuated with a factor of of 10 – 50. Thus if looking for a line at 335.796 GHz with HARP it would be unwise to use the lower sideband (LSB). The strong 12CO line at 345.796 GHz would be in the upper unwanted sideband. Even if HARP is a SSB receiver the CO line is frequently brighter than 20 K so you can still see some remnants of the CO line. Thus care has to be taken when selecting sidebands even for a SSB receiver.

Further, adding data obtained in both USB and LSB requires some care. The frequency scales are inverted and the data needs to be resampled on a uniform frequency scale before the data can be averaged. The reduction software can easily do this but due to the required resampling many observers prefer to use the same sideband for all observations.