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To the digital PSD's, the dynamic reserve is limited by the quality of the A/D conversion. Once the input signal is
digitized, no further errors are introduced. Practically, the dynamic reserve of SE1201 can exceed 120dB.
The performance of a lock-in amplifier is largely determined by the performance of its PSD's. Almost in all respects, the
digital PSD outperforms the analog one. Besides, the digital PSD is also more convenient to modify.
1.5 Time Constants and DC Gain
The output signal of the PSD contains many signals of various frequency, such as the sum or difference between the input
signal frequency and the reference frequency. Only the signal whose frequency is exactly equal to the reference frequency
will result in a DC output.
The low pass filter (LPF) at the PSD output removes all the AC signals that unwanted, including the 2F (sum of the
signal and the reference) and the noise signals. This filter is what makes the lock-in such a narrow band detector.
Time Constants
The bandwidth setting of the low pass filter is the same as the conventional low pass filter. They are both determined by
the time constants. The calculation of the time constant is defined as:
f
TC
2
1
Here f is the -3dB frequency of the low-pass filter. For example, to a one-order low pass filter of RC type, a 1s time
constant means its -3dB point occurs at 0.16Hz.
In fact, where there is an input noise, there is an output noise. By increasing the time constant, the output becomes more
stable and measurement becomes more reliable. The time constant reflects not only the stability of the system and the
accuracy, but also the respond time of the output.
The time constant also determines the equivalent noise bandwidth (ENBW). The ENBW isn't the filter -3dB pole, it is the
effective bandwidth for Gaussian noise.
Digital Filters vs Analog Filters
Analog filters have many limitations in performance. The temperature drift and non-linearity are two important problems
that limit the rolloff performance of an analog filter. A two-stage analog filter provides about a maximum rolloff of 12
dB/oct at high frequency points.
Space and expense are also limitations. Each filter needs to have many different time constant settings. These different
settings require different components and switches to select. Each setting is costly and space consuming. A large quantity
of analog devices also bring quite complexity to the device debugging.
Considering these limitations, we choose a 47 bits digital filter to accomplish narrow band filtering. The DC amplitude is
exactly 0 dB and the equivalent value of Q exceeds 145dB.
Synchronous Filters
