Sensors - Synchronous Detection - Part III - EdsCave

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Sensors - Synchronous Detection - Part III


23 May 2016

Some Additional Thoughts....

In Part 1 and Part 2 of this series I wrote about the basic architecture of synchrounous detection and how it works. In this section I will be writing about some things that go into making a practical system.

Phase Compensation.

In the ideal synchrounous detectors previously considered, the only delay was from the output filter - it was assumed that the sensor and the amplifier had infinite bandwidth.  In reality they will always have some small, but still finite delay.  In the case where you are operating the sensor/amplifier system in a non-synchronous mode, this delay may be small enough in relation to the overall bandwidth of  your measurement that you can ignore it.  In a synchrounous detection system, however, the delay may become a significant problem for two reasons. First, you need to have enough bandwidth to pass the modulated carrier signal through the system, keeping in mind that your carrier will have a frequency that is typically several orders of magnitude higher than the sensed phenomenon.  The second reason is that even if you have adequate bandwidth to pass the carrier signal, introducing any significant phase shift can dramatically affect the amplitude of what comes out of the synchronous detector.  For example,  consider the effect of demodulating a sine wave with another sine wave 90 degrees out-of-phase, as show below:

The demodulated result has double the frequency, but an average value of zero, which is a very different result for the case in which the two sine waves were in phase and the corresponding product  would have an average value of 0.5.  While this is an extreme case (total loss of output signal!), smaller phase shifts will manifest themselves as system scaling errors.  Although one could simply adjust the output scale to compensate, another method is to introduce a parallel phase shift in the carrier reference path (shown below).  One advantage of this approach is that it may be possible to replicate the signal path delay in such a way so as to track phase changes resulting from environmental conditions such as temperature.

Amplifier Offset Error and 1/F Noise

One big set of system-level benefits that I have not mentioned previously are reduction in effective amplifier offset error and 1/F noise.  The amplifier offset error can be thought of a a small DC voltage source (uV to mV range) placed in series with one of the amplifier input terminals.  When used as a DC amplifier, this error is amplified along with the sensor signal.  In the ccase of a synchronouse detector, the amplifier amplifies an AC signal, and the demodulator/filter effectively ignores any DC component on its input.  The end result is that the effect of amplifier offset can be significiantly reduced.

Another related issue is 1/F noise.  Although an amplifier may advertised as having so many nV/sqrt(Hz) of input noise, this metric can vary as a function of frequency.  Typically, as the frequency of interest approaches 0 Hz (DC), the amplifier noise performance gets worse (more noise) in a 1/F manner, with the worst noise density  at low frequency. As luck would have it, low frequencies are often where you want to measure sensor signals.  While this can be a problem with a DC amplifer/filter arrangement, synchrounous detection systems get around this because they modulate the sensor signal up to the carrier frequency, and tend to reject the 1/F noise from tha amplifier in the same way they reject DC amplifier offset.

Note, however, that the magical rejection of DC offset and 1/F noise only applies to that coming from the amplifier. Offset (bridge imbalances) and low-frequency noise originating in your sensor will be treated just as if they were legitimate signal and will be passed along to the output.

Square-Wave Carrier

One technique that can greatly simplify the implementation of a synchronous detector is to use square waves for the carrier as opposed sine waves.  The first way in which this simplifies the electronics is that it is much simpler to generate a square wave than a sine wave, particularly if you are interested in maintaining precise amplitude and symmetry. The second simplification comes from the nature of the demodulator - when using a sine-wave carrier, you need to use a linear multiplier, which is typically an expensive component. when using a square-wave carrier, you only need to mutiply by +1 and -1, which can be done in seveal ways. For a single-ended system, this can be accomplished by an analog switch which selects between the amplified signal (gain = +1) and an inverted version of the amplified signal (gain = -1). In the case of a balanced,  differential system, a DPDT crossover switch can be used to feed the differential signal straight through (gain = +1) or reverse the connections (gain = -1).  

Square-wave Drive can Simplify the Demodulator Hardware

If the Sensor Signals are Balanced,  a DPDT CMOS Switch can Often Serve as a Balanced Demodulator

Because a square-wave carrier contains all odd harmonics (F, 3F, 5F),  this scheme offers more opportunities for external noise to be mis-interpreted as sensor signal. despite this potential shortcoming, the technique can often be made to work well, and having a binary carrier allows for a great deal of implmentation flexibility.
Spread-Spectrum Carrier

So far this series has mostly been concerned with the problem of rejecting 'random' noise sources that might happen to be in the environment, but have not addressed the problem of dealing with deliberate attempts to interfere with the sensor operation.  Injecting an interfering signal at the same frequency and phase of the carrier can be a very effective way of disabling a sensor reliant on synchronous detection.  Some security-related applications have requirements for tamper resistance.  One method of 'tamper-hardening' a synchronous detector is to use a carrier that has been randomized in some way. This is also know as using a spread-spectrum carrier.

While you could use a truly random analog noise source as a carrier, implementing a good one can be a major engineering challenge. Instead, it is typically easier to use what is known as a pseudo-random binary sequence, where the carrier has two levels, like a square wave, but assumes HIGH and LOW states in a manner that appears random.  This effectively 'spreads' the carrier spectrum from a single frequency to a band of frequencies over some range, and is known as 'Direct Sequence Spread Spectrum'.  Another related technique is 'Frequency Hopping Spread Spectrum', in which the carrier frequency changes over time in a pseudo-random manner.

These techniques are particularly useful in sensor systems which are detecting very small changes in quantity being detected and are highly sensitive to external noise. One example is of capacitive proximity sensors.


Synchronous detection is a powerful technique for implmenting sensor systmes that need high levels of noise immunity or need to recover very small signals. In this 3 part series I have outlined the basic concepts for the technique and described how it operates from both time and frequency domain viewpoints. In the final installment I introduced some variations to the basic technique that can often be used to adapt synchronous detection in real-world applications.

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