April 16, 2014

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

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 10NF/10 and A is the numerical power gain, which is equal to 10G/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).

At the receiver antenna, the receiver sensitivity will be a function of the ability of the preselector filter to limit incoming wideband noise and the front-end’s low-noise amplifier (LNA) to provide enough gain to boost signal levels to an acceptable signal-to-noise ratio (SNR) for subsequent signal processing in the RF front end by mixers, demodulators, and/or ADCs.

As with the filters, an RF front-end’s LNAs are specified depending on their location in the signal chain, either for relatively broadband use or for channelized use at the IF stages. An LNA is specified in terms of bandwidth, noise figure, small-signal gain, power supply and power consumption, output power at 1-dB compression, and linearity requirements. The linearity is usually judged in terms of third-order and second-order intercept points to determine the expected behavior of the amplifier when subjected to relatively large-level input signals. Ideally, an LNA can provide sufficient gain to render even low-level signals usable by the RF front-end’s mixers and other components, while also handling high-level signals without excessive distortion.

At one time, LNAs fabricated with gallium arsenide (GaAs) process technology provided optimum performance in terms of noise figure and gain in RF and microwave communications systems. But ever-improving performance in silicon-germanium (SiGe) heterojunction-bipolar-transistor (HBT) now provides comparable or better noise-figure and gain performance in LNAs at frequencies through about 10 GHz.

In contrast to a superheterodyne receiver’s noise, the other end of the dynamic range is the largest signal that the receiver can handle without distortion or, in the case of a digital receiver, degradation of the BER. In a receiver, excessively high signal levels can bring the onset of nonlinear behavior in the receiver’s components, especially the mixers and LNAs. Such nonlinear effects are evidenced as gain compression, intermodulation distortion, and cross modulation, such as AM-to-PM conversion.

At large signal levels, harmonic and intermodulation distortion cause compression and interference that limit the largest signals that a receiver can handle. A receiver’s dynamic range refers to the difference between the MDS and the maximum signal level.

In a single-channel system, the dynamic range is essentially the difference between the 1-dB compressed output power and the output noise floor. The spurious-free dynamic range (SFDR) is defined as the range of input power levels from which the output signal just exceeds the output noise floor, and for which any distortion components remain buried below the noise floor.

IP3
The input third-order intercept point is often used as a measure of component and receiver power-handling capability. As mentioned earlier, it is defined as the extrapolated input power level per tone that would cause the output third-order intermodulation products to equal the single-tone linear fundamental output power.

The output power at that point is the output third-order intercept point. The intercept point is fictitious in that it is necessary to extrapolate the fundamental component in a linear fashion and assume that the third-order intermodulation products increase forever with a 3:1 slope.

In reality, the difference between a component’s actual output power at 1-dB compression and the third-order intercept point can be as little as 6 dB and as much as 20 dB. Along with the third-order intercept point, the second-order intercept point is also used as a measure of power-handling capability of dynamic range. It refers to the fictitious intersection of the second-harmonic output power with the fundamental-frequency output power.

In analyzing a receiver’s dynamic range, it is important to note how the definitions of larger signals can vary. For example, for multiple-carrier communications systems, the peak power level will be much greater than the average power level because of the random phases of the multiple carriers and how they combine in phase. In a multicarrier system, the specified average power may be within the linear region of the system but the peaks may push the system into nonlinear behavior. This nonlinear behavior includes a phenomenon known as spectral regrowth and is characterized by such parameters as adjacent-channel power ratio (ACPR) where the power of a transmitted signal can literally leak into nearby channels because of intermodulation distortion.

Automatic gain control (AGC) can be used in a superheterodyne front end to decrease the gain when strong signals can cause overload or distortion, although there may be trade-offs for the SNR performance. If attenuation is added before the LNA in a receiver front end, for example, it can reduce the risk of nonlinearities caused by large signals at the cost of an increase in noise figure, as noted earlier with the 1-dB attenuator example. An AGC tends to sacrifice small-signal performance to achieve large-signal handling capability.

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