An Introduction to Noise, Linearity, and Dynamic Range in RF and Microwave Receivers

One of the challenges of microwave and RF engineering is a lack of intuition. A mechanical engineer can visualize a rocket, a civil engineer can go and look at a bridge doing its work. Electrical engineers working on optics or power generation can see their work at least a little bit. But it is very difficult to experience the output of a radar system or a 5G transceiver. You can only see the output on a screen after it is interpreted by a computer.

Most of Marki Microwave’s customers make high dynamic range receivers. These receivers are measuring the part of the electromagnetic spectrum that you can’t see. The specifications given in Marki Microwave’s datasheets provide measurements of our components to demonstrate how they will maintain the integrity of a signal against degradation, but it is not immediately clear from reading a datasheet how a particular spec will relate to the end goal of a system. In this note we will discuss the high level goals of our customers in an intuitive way, and then discuss how common microwave component specifications relate to these system goals.

System Specifications: Noise

Most people have an intuitive understanding of noise that is not the same as the definition of noise in electronics. In a crowded room with many people talking you would say there is background ‘noise’. In a room with many radios transmitting at the same time we would say there are ‘interferers’ or ‘blockers’.

Noise in electronic systems refers specifically to random fluctuations in a signal. Most commonly this is caused by random motion of molecules from heat, but it can also be caused by random transit times across semiconductor junctions or the discrete nature of current flows. Key distinctions about noise:

1)      Noise is random, and therefore cannot be corrected

2)      Noise sets the fundamental limit to the lowest power signal that can be detected

3)      Noise occurs across frequencies

The ability to detect a signal in a receiver depends on the signal to noise ratio. This is primarily set at the input to the receiver. The noise into the receiver is constant regardless of input signal power. Noise can be added throughout the receiver, but most noise at the output is just amplified noise from the input (typically an antenna in an RF system).

Noise is commonly confused with the next specification, nonlinear distortion.

System Specification: Nonlinear Distortion

Nonlinear distortion occurs when an input signal has more power than a system can process linearly. Nonlinear distortion is easily demonstrated using an electric guitar.

Distortion occurs when the input power to a nonlinear component (typically an amplifier, mixer, or analog to digital converter) is high relative to the power handling of the component. Noise is typically broadband or white, meaning that it occurs across frequencies, while distortion occurs at specific harmonics of an input frequency.

The important distinctions about nonlinear distortion are:

1)      Nonlinear distortion is predictable if you know the input signal and the response of the component, so it can be corrected

2)      Nonlinear distortion limits the highest power signal that can be processed

3)      Nonlinear distortion occurs at specific harmonic frequencies of the input signal

There is one other class of signal impairments that must be considered.

System Specification: Signal Integrity

Signal integrity is a broad term that includes noise, nonlinear distortion, and linear distortion. Effects like echoes, dispersion (when different frequencies arrive at different times), multi-path, and other aberrations cause the signal to arrive distorted. These distortions are at the same frequency, but still cause the signal to be undetectable.

Noise and Distortion in Video Signals

In this image the desired signal (an image of a person in a suit and a hat maybe?) is undetectable due to noise. Additionally, linear distortion in the signal is evident from the jagged line on the right hand side. This might be a door, or the edge of a wall, but we can’t tell because the signal is distorted and noisy.

In this image the source of distortion is the most basic nonlinear distortion – saturation. The image sensor - a typical charged coupled device (CCD) sensor – is overloaded with too much light. If we were trying to see an object close to the sun in this image (perhaps an approaching airplane), we wouldn’t be able to distinguish it because of the nonlinear distortion.

Noise and Distortion in Audio Systems

Noise and Distortion in Microwave Component Specifications

This video demonstrates what different signal distortions sound like. The guitar is the signal of interest/source (radio wave in the air), the pedals and amplifier are the RF chain, and our ears are the receiver/ADC interpreting data after processing by a computer.

• Test 1 shows linear amp with minimal distortion and our ears can receive each note clearly.
• Test 2 lowers the signal level and increases the amplifier gain which results in our ears straining to hear the clear tone above the amplified noise on the input. 
• Test 3 increases the input signal power into a saturated RF chain/amplifier causing our ears to struggle to discern the fundamental tone due to all of the harmonics generated by saturating the amplifier.
• Test 4 uses various delay pedals to show the impact of delay (a type of linear distortion) on the signal.
• Last is an example of oscillations. 

Noise and Distortion in Microwave Component Specifications

Most of the performance specifications on a microwave or RF component relate to the end goals stated above.

Parameters that Quantify the Effect on Signal to Noise Ratio:

Insertion Loss – The loss of a component will reduce the signal power in a receiver. However, if the component follows an element with gain (in particular a low noise amplifier) the noise power will be reduced by approximately the same amount. It is only when the amplified noise level starts to approach the thermal noise floor that insertion loss will affect the signal to noise ratio.

Conversion Loss – Similar to insertion loss, conversion loss only affects the signal to noise ratio when the amplified noise power density is close to the thermal floor.

Noise Figure/Noise Factor/Equivalent Noise Temperature – In an amplifier these parameters all refer to the same thing, which is how much additional white noise is added to an input signal, in addition to the amplified input noise. Again this is only important when the amplified input noise is low, particularly at the very front end of a receiver where the noise is at the thermal noise floor. This is also how noise figure is defined. The way that noise propagates in a system is expressed by Friis theory for cascaded noise figure, which clearly shows that the noise figure of a system is dominated by the noise figure of the initial components. 

In lossy components the noise figure is equivalent to the insertion or conversion loss. This works for calculations, but it is a logical error to conclude that these components add noise. While all components add a small amount of thermal noise, this is only relevant when the amplified noise level is extremely low.

Similar to how loss does not affect the signal to noise ratio unless the noise is close to the noise floor, gain does not affect the signal to noise ratio. This is because the gain of an amplifier applies to both the signal and the noise equally. There is noise added (according to the noise figure), but the noise is equally amplified by the gain.

The way that noise propagates in a system is expressed by Friis theory for cascaded noise figure, which clearly shows that the noise figure of a system is dominated by the noise figure of the initial components. 

Parameters that Quantify Nonlinear Distortion

Power Compression – This is most commonly the 1 dB power compression point (P1dB), but sometimes the 3dB (P3dB) or 0.1 dB  (P0.1dB) point is specified. This expresses how much input power can be processed linearly without causing saturation.

Second and Third Order Intercept – When multiple tones are input, they create amplitude peaks and valleys, which compress the system. In addition to compression, different circuit parameters can be affected by input power that cause multiple tones in an amplifier, mixer, switch, or limiter to create harmonic products. These are quantified by the third order intercept point, which is just a convenient mathematical concept to measure this effect.

Spurious Outputs- These are specific to mixers, and relate to the nonlinear distortion that occurs when a high power input signal intermodulates with the switching tone in the mixer (the local oscillator or LO). These products occur at various frequencies and will cause distortion if they are not filtered out.

Parameters that Quantify Linear Distortion

Return Loss and VSWR- Return loss quantifies the reflections from the various ports on a component. Reflections of the signal cause distortions similar to echoes in audio systems and double images in video systems.

 Isolation, Suppression, and Directivity – When a loss applies to an undesired signal, it is referred to as isolation. When isolation of an undesired signal is related to the desired signal it is called suppression. When it is specifically the suppression of the reverse signal in a coupler, it is called directivity. Undesired signals obviously distort the desired signal by creating unwanted images.

Group Delay Flatness – Dispersion occurs when different frequencies travel at different speeds, and arrive at the detector at different times. This causes distortion at the output. This is quantified by the group delay, or the amount of time it takes for a signal to traverse a component. The absolute delay is usually unimportant, but the flatness of the group delay indicates how much distortion will occur. This is typically calibrated digitally in modern systems, but this requires digital resources.

Conclusion

It is hoped that understanding how various component performance parameters for RF and microwave components will lead to a better appreciation for the value of high performance components. This is the exclusive focus of Marki Microwave: creating broadband, high performance components that allow system designers to create systems that have the highest signal integrity of any systems in the world.