An introduction to synchronous detection
A.Platil
Overview:
• Properties of SD
• Fourier transform and spectra
• General synchronous detector
(AKA lock-in amplifier, syn. demodulator, Phase Sensitive Detector)
• Switching mode SD: pros and cons
• Sensor applications of SD:
– infrared pyrometer elements with chopper modulator
– AC mode strain gauge excitation
Introduction:
Synchronous detection is a signal processing technique that:
• Makes possible extracting even weak signal in strong noise
background - e.g.:
– Radio communication
– Strongly disturbed signals in industry
• Requires reference signal with known frequency and phase
For starters: brief refresh of Fourier transform
Fourier transform and signal spectrum
A
f
t
Časová
Time
doména
domain
Frekvenční
Freqency
doména
domain
Signal spectrum
• Any periodic signal can be described as a combination of
harmonic signals of various amplitude and phase:
x(t ) = X 0 +
∑X
k =1, 2 , ...
k
sin( k ω t + ϕ k )
• Signal spectra are measured with spectral analyzers of
various types, e.g. analogue swept-filter or digital FFT
analyzers
Example1 - harmonic signal + weak noise, f = 100 Hz,
spectrum consists of one peak at 100 Hz, noise floor is -90 dB
Example 2: Combination of two harmonic signals 100 Hz and
300 Hz. Spectrum consists of two peaks.
Example 3: Square wave signal, spectrum consists of all odd
higher harmonic components
1st, 3rd, 5th, etc. higher harmonic components of square wave signal
Example 4: Amplitude modulation. Carrier frequency 50 kHz,
signal (information) frequency 5 kHz.
In the spectrum of an AM-modulated signal, there is one peak of
the carrier f0 and two side-peaks at combination (additive and
subtractive) frequencies f0+/-fm.
Synchronous detector – can be used in situations where we
know exact frequency and phase of signal.
E.g. Where the experiment excitation frequency is available
as reference.
Excitation
Generator
Reference
signal f
Experiment produces output
signal synchronous to excitation
at frequencies k x f
f
Experiment
Measurement
(sync. detection)
... or where the signal is modulated by known frequency before
further processing - e.g.: modulating (chopper) amplifier
Low level DC voltage amplification (µV)
- problem: DC amplifier offset and its drift
-solution: modulation of DC signal (by chopper), amplification by
AC amplifier (DC offset drift is not an issue) and demodulation
Example of synchronous detection: receiver of AM radio –
superheterodyne receiver (simplified)
Směšovač
Mixer
(násobička)
f
(multiplier)
Referenční
Local
oscilátor (f0)
oscillator
f0
Dolní propust
Low-pass
filter
Zesílení
Audio
signálu
f2
amplifier
f1 = f + f0
f2 = f – f0
On input: all RF signals captured by antenna, including wanted radio
station at f0
After mixer: combination frequencies f1 a f2.
After Low-pass: only narrow band of low frequency signals
• In the mixer output, there are various combination
(additive and subtractive) frequencies corresponding to
signals captured by antenna
• Special case for f = f0 (local oscillator is tuned to wanted
station at f0)
– subtractive frequency is zero (we get DC signal
proportional to amplitude of received RF signal at f0)
Case 1: station transmits “silence”or a DC signal, the RF signal
spectrum consists only of the station carrier, e.g. 100 kHz.
After mixer (multiplier) tuned exactly to 100kHz we get combination
frequencies:
f1 = f + f0 = f0 + f0 = 2f0 (additive frequency, rejected by LP filter) and
f2 = f – f0 = f0 – f0 = 0 Hz
The DC signal gets through LP filter to output (together with remnants
of noise that fits into the LP band – according to LP bandwidth)
A
DP filtr
LP
A
100 kHz
Signal at mixer input
f
0 Hz
200 kHz
f
Signals at mixer output, LP
filter bandwidth is suggested
Case 2: station transmits a tune e.g. 10 kHz
the RF signal spectrum consists of 100 kHz carrier
with side bands (90 kHz a 110 kHz).
After mixer (multiplier) with local oscillator exactly tuned to 100kHz
we get combination frequencies:
f1 = f + f0 = f0 + f0 = 200 kHz +/- 10 kHz (rejected by LP filter) and
f2 = f – f0 = f0 – f0 = 10 kHz
Signal 10 kHz pass through LP (provided the LP has adequate BW)
DP filtr
A
A
100 kHz
f
Signal at mixer input
0 Hz
10 kHz
200 kHz
f
Signals at mixer output, LP
filter bandwidth is suggested
The bandwidth of low-pass filter after mixer determines the
resulting sensitive BW of the synchronous detector.
The local oscillator determines the resulting center frequency
of sensitive BW of the synchronous detector.
Local oscillator frequency f0
P ro p u s tn é p á s m o
LP
fre k v e n c e
frequency
bandwidth
Tradeoff:
the lower LP bandwidth, the less noise makes it to the output
BUT
the slower is the response to useful signal changes (useful BW)
Mathematical background of SD:
The measured and the reference signals are:
U sig ⋅ sin (ω sig ⋅ t + Θ sig )
U ref ⋅ sin (ω ref ⋅ t + Θ ref )
Then signal after mixer (multiplier) is:
U Mix. = U sig ⋅ U ref ⋅ sin (ω sig ⋅ t + Θ sig )⋅ sin (ωref ⋅ t + Θ ref ) =
[
]
} Low freq.
[
]
} High
1
= ⋅ U sig ⋅ U ref ⋅ cos( ω sig − ωref ⋅ t + Θ sig − Θ ref ) −
2
1
− ⋅ U sig ⋅ U ref ⋅ cos( ω sig + ωref ⋅ t + Θ sig + Θ ref )
2
Note: see that output amplitude is influenced by phase
freq.
(rejected)
The preceding example: detection with harmonic reference signal
BUT
In practice: often detection with squarewave reference (switchingmode detection)
signal
Phase Sensitive Detector
(switching-mode detector)
x
x / -x
reference
Signal after multiplier
Signal after LP filter
Remember – phase does matter
If the reference is shifted by 90°, the detected signal is completely
changed and the filtered value is zero (compare with previous fig.)
signal
Phase Sensitive Detector
(switching-mode detector)
Signal after multiplier
Signal after LP filter
x
x / -x
reference
Note: for signal frequencies that do not match the reference
frequency the system throughput is close to zero.
Synchronous demodulator in general:
x(t)
multiplier
signal
v(t)
Mean value
calculation
reference
r(t)
1. analogue multiplier = ideal,
BUT: non-linearity, expensive
2. Switching circuit
BUT: sensitivity to odd harmonics
v(t)=K(t).x(t)
K(t)... switching funct.
Low pass filter
Or integrator
1
T
T
∫ v (t )
0
output
Pros and cons of switching-mode synchr. detection
+ : simple realization, cheap solution, even for large signals
– : sensitivity even to other frequencies than fref
Reason: multiplying with squarewave, the spectrum of which consists
of ALL odd higher harmonics: 1st , 3rd , 5th , 7th , ...
The resulting set of sensitive bandwidths of switching-mode SD
Switching function (reference) = symmetrical squarewave
Switching perioda T=2π/Ω
Sensor applications of SD
• AC biased strain-gauge bridge:
– Low level signals => AC signal is easier to process than
DC signal (offset drift, ...).
– Signal processing with a synchr. detector => noise
rejection
– Switching-mode SD sensitive to other frequencies (/)
• Pyrometry (contactless detection of infrared heat):
– Lot of noise, difficult to separate from useful signal
– Signal (IR radiation) from observed object is
periodically interrupted with a chopping shutter
– Signal processing with a synchr. detector with a
reference from shutter
Conclusion
• Synchronous detection enables processing of very weak
signals (even orders of magnitude lower than noise)
• Synchronous detector is sensitive on the frequency of
reference (e.g from local oscillator) in a narrow band
(given by LP filter)
• Switching-mode detection is simple and cheap, but then we
get sensitivity also on all higher odd harmonics of the
reference.