Stanford Research Systems SR865A, Руководство по эксплуатации

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38 Basics Chapter 2
SR865A DSP Lock-in Amplifier
The SR865A generates its own sine wave at frequency f
L
, shown as the lock-in reference
below. The lock-in reference is sin( ω
L
t + θ
ref
) where ω
L
= 2πf
L
.
The SR865A amplifies the signal and then multiplies it by the lock-in reference using a
phase-sensitive detector (PSD) or multiplier. The output of the PSD is simply the product
of two sine waves.
V
psd
= V
sig
sin(ω
r
t + θ
sig
) sin(ω
L
t + θ
ref
)
= 1/2 V
sig
cos([ω
r
− ω
L
]t + θ
sig
− θ
ref
) −
1/2 V
sig
cos([ω
r
+ ω
L
]t + θ
sig
+ θ
ref
)
The PSD output is two ac signals, one at the difference frequency (ω
r
− ω
L
) and the other
at the sum frequency (ω
r
+ ω
L
).
If the PSD output is passed through a low pass filter, the ac signals are removed. What
will be left? In the general case, nothing. However, if ω
r
equals ω
L
, the difference
frequency component will be a dc signal. In this case, the filtered PSD output will be
V
psd
= 1/2 V
sig
cos(θ
sig
− θ
ref
)
This is a very nice signal — it is a dc signal proportional to the signal amplitude.
Narrow band detection
Now suppose the input is made up of signal plus noise. The PSD and low pass filter only
detect signals whose frequencies are very close to the lock-in reference frequency. Noise
signals at frequencies far from the reference are attenuated at the PSD output by the low
pass filter (neither ω
noise
− ω
ref
nor ω
noise
+
ω
ref
are close to dc). Noise at frequencies very
close to the reference frequency will result in very low frequency ac outputs from the
PSD (|ω
noise
− ω
ref
| is small). Their attenuation depends upon the low pass filter bandwidth
and roll-off. A narrower bandwidth will remove noise sources very close to the reference
frequency, a wider bandwidth allows these signals to pass. The low pass filter bandwidth
determines the bandwidth of detection. Only the signal at the reference frequency will