A Practical Guide To Noise In Frequency Conversions

In a typical receiver application, a frequency conversion is performed after filtering and low noise amplification. This frequency conversion can have a significant impact on the noise figure of the receiver, but it doesn’t have to.

_{Fig 1: Basic Receiver Block Diagram}

As all our mixer datasheets state, “Mixer Noise Figure typically measures within 0.5 dB of conversion loss for IF frequencies greater than 5 MHz”. This simple statement obscures a more complicated reality. When RF engineers encounter noise figure problems with the receiver, they can mistakenly conclude that the mixer is not performing properly.

In this article we will illuminate potentially overlooked sources of noise in a typical converter.

Noise Basics

Noise, or random signal fluctuations, will be present in any real system due to the thermal energy generated from the random motion of electrons. We can classify noise in two forms: Additive White Gaussian Noise (AWGN) and frequency dependent noise. AWGN includes both thermal noise (aka Johnson noise) and shot noise, while frequency dependent noise includes flicker noise (  noise) and integrated flicker noise (noise of the form of ). But why does this matter? Noise limits the minimum detectable signal of a communications system. You are limited by your noise floor; you need to be able to discriminate an intentional output from random information.

Frequency Dependent Noise

Our datasheets claim that “Mixer Noise Figure typically measures within 0.5 dB of conversion loss for IF frequencies greater than 5 MHz”. Why the frequency dependence?

When IF frequencies below 5 MHz are used, the phase noise contribution of the converter becomes dominant. Phase noise in converters can come from the LO phase noise or the flicker noise of the nonlinear mixer elements themselves. Above 5 MHz the noise of the converter is typically dominated by the white noise and phase noise contributions can be neglected.

_{Fig 2: Noise Figure Contributions from a Converter}

For the purpose of this post, let’s assume we’re using a mixer to downconvert an incoming RF signal with a low-side LO to generate an output signal at f_IF. An ideal mixer will take two signals as inputs and output a third signal at a frequency equal to the sum or difference of the two inputs; in our case our IF signal will be located at f_RF-f_LO. Unfortunately, our RF and LO sources will not be perfect single tones and our mixer will convert and pass through any signal that’s presented to it with a finite loss, whether desired signal or noise from the RF or the LO.

Noise contribution from RF source

_{Fig 3: Noise Contributions from the RF Input}

In terms of RF contributions, noise in our IF band can result from:

1. Noise at the desired RF band f_RF
2. Noise at the image band f_LO (+ or -) f_IF
3. Noise at the IF frequency f_IF

• f_RF: In a typical receiver the input to the mixer will have excess noise (above the thermal floor) due to the front end low noise amplifier (LNA). This noise will be downconverted to the IF band with the same conversion loss as our desired RF signal. If the gain plus noise figure of the LNA is much greater than the conversion loss of the mixer then the RF noise will have the same loss as the RF signal, so the signal to noise ratio (SNR) at the output is the same as the SNR at the input. If the signal input noise is thermally limited (as in the definition of noise figure), the signal and noise will still be attenuated by the same amount but new (and indistinguishable) noise will be added to the output signal by the mixer. This is the source of the noise figure in a mixer, as in an attenuator.

• f_LO (+ or -) f_IF : Our RF band is not the only band that can downconvert to our IF; we have an image problem as well. The image frequency is spaced f_IF away from our LO, just like our RF signal, but on the opposite side. Any noise at the image frequency will also mix with the LO and convert to f_IF. Unlike signal noise, this can be reduced or eliminated with an image rejection filter or by using an image reject mixer if a filter is not feasible. If the conversion loss of the mixer plus rejection of any subsequent filtering is greater than the gain plus noise figure of the LNA, then this noise will not degrade the receiver noise figure.

• f_IF: Noise at the frequency of our IF present at the RF port of our mixer can pass directly through to the IF port of our mixer. For mixers, the RF to IF isolation is a measure of the insertion loss from the RF port to the IF port. This noise is typically rejected by channel selection filtering in all but the widest bandwidth receivers. However, if the gain of the LNA at the IF frequency is higher than the RF-IF isolation (and there is no subsequent filtering) there will be some noise contribution from this effect.

When will out of band RF noise sources affect the converter noise figure?

In the absence of a signal or LO input, a mixer will still output thermal limited noise power. The value of this noise power N can be calculated by the simple formula kTB where T is the temperature, B is the bandwidth, k is Boltzmann’s constant, and kT at room temperature ~ -174 dBm.

It’s very common for an LNA to be present near the front of a receiver to amplify an incoming RF signal. The noise floor around our output is dependent on both the gain and noise figure of the LNA on the RF signal chain as well as the conversion loss and R-I isolation of our mixer. The gain and NF add to our noise floor, while the mixer losses lower it accordingly.

As mentioned above, this thermal noise is the source of the noise figure of a mixer (or any lossy element). However, noise from the out-of-band frequencies in the RF signal input can add more than the thermal noise, degrading the noise figure of the receiver. This happens when the noise isolation of the mixer (the conversion loss of the image or the RF-IF isolation) is less than the noise addition of the LNA (given by the gain plus noise figure).

_{Fig 4: Illustration of Criteria for RF noise Addition}

Noise Contribution from LO source

_{Fig 5: Noise Contributions from the LO drive}

In addition to the commonly understood noise coming from the receiver, less well understood is the noise contribution of the local oscillator (LO). In terms of LO contributions, noise in our IF band can result from:

4. Noise at f_LO+f_IF remixing with the LO (Common Mode)
5. Noise at f_LO-f_IF remixing with the LO (Common Mode)
6. Noise at f_IF feeding through the mixer (LO to IF leakage)

• f_LO±f_IF We already know from the RF case that noise at the RF band and image band can mix with the LO and downconvert to the IF band; however, what is less intuitive is that the same exact thing can happen at the LO port of our mixer. Due to reflections within our converters, noise present at these frequencies (f_LO+f_IF) can remix with the LO and downconvert to our IF.

How to measure common mode conversion loss

The technique to measure common mode conversion loss in a mixer is to inject a low power pilot tone, representative of noise, along with the large tone into the LO port of the mixer and measure the output power at f_IF .

_{Fig 6: Experimental Setup to Measure Common Mode Downconversion}

Using our MM1-1467Hv mixer and C16-0140 coupler, we set up the following two tests to measure the common mode loss of such noise. We downconverted our desired 38.49 GHz RF signal to a 7.99 GHz IF using a 30.5 GHz LO.

_{Fig 7: Illustration of Common Mode Noise Addition}

Using -10 dBm pilot tones at 22.49 GHz and 38.51 GHz coupled to our 30.5 GHz LO, we measured the strength of 8.01 GHz tones (as a representation of in-band noise) relative to our desired 7.99 GHz IF output. For the -10 dBm pilot tones, the signal power of the resulting noisy IF signals were -56 dBm and -59 dBm respectively. This give a common mode downconversion loss of 46 and 49 dB.

The common mode downconversion can be thought of as LO power that leaks through to the RF, where it is downconverted to the IF. This leads to the common

Rule of Thumb: Common mode conversion loss can be estimated as the sum of the LO to RF isolation plus the conversion loss in dB.

The above experiments show that this rule of thumb is in the right neighborhood, but not as accurate as a measurement.

• f_IF : Similar to the RF case, part of the noise at the IF results from direct LO to IF leakage. Noise at f_IF present at the LO port of our mixer can pass directly through to the IF port of our mixer. For mixers, the LO to IF isolation is a measure of the insertion loss from the LO port to the IF port. This noise can also be rejected by channel selection filtering in all but the widest bandwidth receivers.

When will LO noise sources affect the converter noise figure?

_{Fig 8: Illustration of Criteria for Noise Addition from the LO}

Like the RF noise case, the gain and noise figure of an LO driver amplifier will amplify the in-band noise and will contribute its own noise figure to it, while the common mode losses and L-I isolation attenuates the noisy signal accordingly. Unlike the RF case, the noise input to the LO comes from an oscillator or synthesizer, and it is unlikely to be thermally limited. This means that the common mode conversion loss or L-I isolation needs to be high enough that it not only suppresses the contributions of the LO amplifier, but pushes the synthesizer noise below the thermal noise floor.

Noise contribution from LO driver amplifier

It is common to use amplifiers to amplify our LO to a high enough power to drive our mixers. Unfortunately, any noise in band of our amplifier will get amplified just the same as our signal. As a result, an amplifier can increase the noise floor of a system, degrading our output SNR.

_{Fig 9: Noise Output From an Amplifier Follows Gain Profile}

When determining the noise contribution from our amplifiers, it is important to understand that the typical gain that’s reported for amplifiers will not necessarily be a constant value across band, but rather an average across the band of the amplifier. For this reason, gain vs frequency will result in noise power that varies with frequency (Watts/Hz) dependent on the amplifier that is used. This is particularly important for noise at f_IF, which may be out of the operating band of the LO amplifier and at a frequency that is not well specified. The LO amplifier may supply significant attenuation, or it may supply gain.

Unlike signal path amplifiers, and LO driver amplifier is typically operated in continuous compression. For an amplifier operating in compression, the gain and noise figure will be different than that of an amplifier that is operated linearly. The gain of the amplifier is (by definition) reduced in compression, so the amplified noise is reduced. Amplitude noise can be converted to phase noise due to compression effects. For extremely high performance RF systems you may need to consider these effects and design with large signal operation in mind.

Conclusion

All these noise sources need to be carefully accounted for as they all contribute to the total noise observed at our IF band. In addition to monitoring these noise sources and filtering (if necessary), the best way to combat noise addition in a converter is to select a mixer with high isolations. As you can see above all three isolations (LO to IF, RF to IF, and LO to RF through common mode mixing) can improve the noise performance of a converter.

Marki has a broad selection of high isolation mixers covering every frequency from 1 to 110 GHz. For details or assistance with mixer selection please contact support@markimicrowave.com.