# Noise Figure of a Mixer

It is industry practice to consider the Noise Figure (NF) of a Mixer equal to its conversion loss. This is a useful approximation, and it’s generally accurate within 0.5 dB, or, at any rate, within the uncertainty of a typical noise figure measurement.

Rationale Behind this Industry Practice

The reason behind this approximation is that the noise figure of any perfectly matched passive device is equal to its insertion loss if its physical temperature is the same as that of the system.

What if the device is not perfectly matched and a measurable VSWR is present at the RF and IF ports?

Let’s assume that the VSWR at one of the ports is 2:1, which corresponds to a Return Loss on that port of 9.5 dB. The mismatch loss resulting from that standing wave is about 0.5 dB. A VSWR of 2:1, although is not impeccable, is a relatively common value to experiment on a real system, and so is its mismatch loss.

The Conversion Loss of a non-perfectly matched, two-port passive device–be it a Mixer at its RF and IF ports, or a Fixed Attenuator–in a matched system, is the sum of the Insertion Loss (attenuation) of the component and its Mismatch loss. The Noise Figure will be equal to the total Insertion Loss. Considering an ideal mixer with 10 dB of Conversion Loss and a port VSWR of 2:1, the Noise Figure will be in the order of 9.5 dB.

However, the relation of Noise Figure and Insertion Loss measurements will be subject to how well matched your system is compared to those used to measure the Conversion Loss, and that matching varies over frequency. The rule of thumb of Noise Figure = Insertion Loss ± 0.5 dB becomes useful in these realistic scenarios.

Double Sideband Mixers

The Dual Sideband (DSB) NF of a mixer is what is stated in the datasheet or what can be derived using the rule of thumb above. In this frequency conversion scheme, the RF signal is present at both images, which are converted to the same IF frequency.

Single Sideband Noise Figure

Let us take a down-conversion scheme to an IF frequency > 0 (finite IF), using a balanced mixer like model SFB-67310410-1010KF-N3. This mixer down-converts an extended RF range, from 65 to 100 GHz with a fixed LO at 102.5 GHz. If our RF signal is centered at 94 GHz, the IF frequency will be IF = |LO-RF| = 8.5 GHz. The conversion loss is about 7.5 dB. However, when we use a full-W band Noise Source and measure the Noise Figure, we measure a value 3 dB higher than the conversion loss. What is happening?

When using the Y-factor method with a full band noise source like STZ-75311418-10-I1, we should always keep in mind where our image frequency is. In this case, the image frequency is 111 GHz, which is right above the W band, and with all confidence our Noise Source will still have a non-zero, or even almost nominal, ENR. The noise power generated at the upper side band will fold down to our IF frequency, effectively doubling the noise power and reducing the SNR by 3dB, that is, increasing the Noise Figure by 3 dB. This mechanism is called Noise Folding.