Radio Architectures, Pt 4: sensitivity, noise, front-end amplifiers

Click here for "What's in an RF Front End?"
Click here for "Understand Radio Architectures, Part 1"
Click here for "Radio Architectures, Pt 2: Receivers, LOs, and Mixers"
Click here for "Radio Architectures, Pt 3: Intermodulation and Intercept Points"
Click here for "Radio Architectures, Pt 5: ADCs and Receivers"

System sensitivity and noise
The noise from each component in the front end adds to the receiver's noise floor, which sets the limit on the minimum signal level that can be detected. Noise can be characterized by its power spectral density (PSD), which is the power contained within a given bandwidth and is presented in units of watts per hertz.

Every electronic component contributes some amount of noise to a receiving system, with the minimum amount of noise related to temperature known as the system's thermal noise, or kTB, where k is Boltzmann's constant 1.38-10'20 mW/K, T is the temperature in degrees Kelvin (K), and B is the noise bandwidth (in Hz).

At room temperature, the thermal noise generated in a 1-Hz bandwidth is:

With an increase in bandwidth comes an increase in noise power and thus the importance of filtering in a superheterodyne receiver as a means of limiting the noise power. For this reason, the final IF filter in a superheterodyne receiver is made as narrow as possible to support the channel reception and to limit the amount of noise in the channel just prior to demodulation and detection. The final IF filter determines the noise bandwidth of the receiver, since it will be the most narrowband component in the front-end analog signal chain prior to detection.

Front-end receiver components are characterized in terms of noise by several parameters, including noise figure (NF) and noise factor (F). For the receiver as a whole, the noise factor is simply a ratio of the SNR at the output of the receiver compared to the SNR at the source of the receiver. For each component, similarly, the noise factor is the ratio of the SNR at the output to the SNR at the input. The noise figure is identical to the noise factor, except that it is given in dB. The noise factor is a pure ratio:

where SNR₂ is the output SNR of a component, device, or receiver and SNR₁ is the input SNR of the component, device, or receiver. If an amplifier was ideal or a component completely without noise, its noise figure would equal 0 dB. In reality, the noise figure of an amplifier or component is always positive.

For a passive device, the noise figure is equal to the insertion loss of the device. For example, the noise figure of a 1-dB attenuator without losses beyond the attenuation value is 1 dB. In a superheterodyne front end, the noise power of the components that are connected or cascaded together rises from the input to the output as the noise from succeeding stages is added to the system. In a simple calculation of how the noise contributions of front-end stages add together, there is the well-known Friis's equation:

where F =the noise factor, which is equivalent to 10^NF/10 and A is the numerical power gain, which is equal to 10^G/10 where G is the power gain is dB. From this equation, it can be seen how the noise factor of the first stage in the system (F₁) has a dominant effect on the overall noise performance of the receiver system.

Noise factor can be used in the calculation of the overall added noise of a series of cascaded components in a receiver, using the gain and noise factor values of the different components:

where the F parameters represent the noise factor values of the different front-end stages and the A parameters represent the numeric power gain levels of the different front-end stages. A quick look at this equation again shows the weight of the first noise stage on the overall noise factor. In a receiver with five noise-contributing stages (n=5), for example, the noise of the final stages is greatly reduced by the combined gain of the components.

The noise floor of a receiver determines its sensitivity to low-level signals and its capability of detecting and demodulating those signals. The input referred noise level (noise at the antenna prior to the addition of noise by the other analog components in the receiver front end) is sometimes referred to as the minimum detectable signal (MDS).

In some cases, a parameter known as signal in noise and distortion (SINAD) may also be used to characterize a receiver's noise performance, especially with a need to account for signals with noiselike distortion components. This parameter includes carrier-generated harmonics and other nonlinear distortion components in an evaluation of receiver sensitivity.

In a digital system, it is simpler to measure the bit-error rate (BER) induced by noise when a signal is weak. The BER affects the data rate so it is a more useful performance measure than the SNR for evaluating receiver sensitivity. With BER, the receiver's sensitivity can be referenced to a particular BER value. Typically a BER of 0.1% (e.g., in the GSM standard) is specified and the sensitivity of the receiver is measured by adjusting the level of the input signal until this BER is achieved at the output of the receiver.

A front end's noise floor is principally established by noise in components such as thermal noise, shot noise and flicker noise. At the same time, any decrease in gain will increase the noise floor. Thus, there must be enough margins in the system SNR to allow for a reduction in gain when making adjustments in gain for larger-level signals.

Front-End Amplifiers
The RF front-end component most commonly connected to an RF or IF filter is an RF or IF amplifier, respectively. Depending upon its function in the system, this amplifier may be designed for high output power (in the transmitter) or low-noise performance (in the receiver).