Receivers
A 200 kHz receiver with a 6 dB noise figure hears down to −105 dBm, but two neighbors at −45 dBm already fill its channel with intermodulation. The dynamic range lies between those two numbers.
01The superheterodyne receiver and its successors
A receiver has to find a weak signal among others that are much stronger. The superheterodyne, invented by Edwin Armstrong in 1918, solves it with a mixer that translates each channel to a fixed intermediate frequency, where a selective filter and an amplifier with automatic gain control do the work. Current integrated receivers also use direct conversion, which brings the channel down to baseband with an I/Q demodulator, or the low-IF approach, and do the channel filtering digitally. Whatever the architecture, three figures describe it: sensitivity, selectivity and dynamic range.
02Sensitivity
The weakest signal that the receiver can demodulate with the required quality is set by the thermal noise, the bandwidth and the noise figure of the chain, computed with the Friis formula from the introduction of Communication Systems:
03Dynamic range and intermodulation
At the upper end, the limit is set by strong signals. Two signals in neighboring channels generate third-order intermodulation products that can fall on the desired channel. Referred to the input, they grow 3 dB for each dB of the signals, and the line meets that of the fundamental at the input intercept point IIP3. The spurious-free dynamic range is the difference between the strongest signal that produces no intermodulation visible above the floor and that floor:
Everything referred to the receiver input. The blue line is the signal; the red one, the third-order intermodulation product with two tones of equal level; the gray line, the noise floor. The spurious-free dynamic range goes from the floor to the level at which the intermodulation reaches it.
04Selectivity and blocking
Selectivity is the ability to reject a strong adjacent channel, and it is provided by IF or digital filters. But a very strong signal can cause trouble even if the filter rejects it: it compresses the input amplifier (blocking), or it mixes with the phase noise of the local oscillator and translates it onto the desired channel (reciprocal mixing). That is why the phase noise of oscillators is a receiver specification.
05In the lab
Measure the sensitivity of an FM receiver by lowering the level of a generator until the audio signal-to-noise ratio falls to 12 dB SINAD, and compare it with the calculated one.
Apply two out-of-channel tones whose third-order product falls in the channel, and measure the level that makes it audible. Calculate IIP3.
With a desired signal near the sensitivity, raise a signal 1 MHz away until the desired one degrades by 3 dB.
06Common mistakes
- Maximizing the input gain. It improves the noise figure, but worsens the linearity of the whole receiver.
- Forgetting the bandwidth in the sensitivity. A channel ten times wider has a floor 10 dB higher.
- Ignoring the phase noise of the local oscillator. With strong neighboring signals, reciprocal mixing masks the weak one.
- Confusing IIP3 with OIP3. They differ by the gain of the chain.
07Self-assessment
What noise floor does a receiver with a 1 MHz bandwidth and a 3 dB noise figure have?
\( -174 + 60 + 3 = -111 \) dBm.
With that floor and IIP3 = −5 dBm, what is the SFDR?
\( \tfrac23 (-5 + 111) \approx 70.7 \) dB.
What is reciprocal mixing?
The translation of the local oscillator's phase noise onto the desired channel, caused by a strong neighboring signal.
What advantage does direct conversion have?
It has no image frequency and is easily integrated, with channel filtering at baseband.
08Further reading
- Behzad Razavi. RF Microelectronics. 2nd ed., Prentice Hall, 2011. Receiver architectures, sensitivity and dynamic range.
- Kevin McClaning. Wireless Receiver Design for Digital Communications. 2nd ed., SciTech, 2012. The design of the receive chain with its noise and linearity budgets.
- Ulrich L. Rohde and Jerry C. Whitaker. Communications Receivers: DSP, Software Radios, and Design. 3rd ed., McGraw-Hill, 2001. The classic reference on receivers, from the superheterodyne to software-defined radio.