What Is Dynamic Reserve; Wide And Close Reserves - Stanford Research Systems SR844 User Manual

SR844 Basics 2-17

What is Dynamic Reserve ?

Dynamic reserve is an important concept for lock-in amplifiers. It is a measure of how
much noise, or interfering signals at frequencies other than the reference, the instrument
can withstand while still accurately measuring the desired signal at the reference
frequency. More dynamic reserve is better. The traditional definition of dynamic reserve
is the ratio of the largest tolerable noise signal (at the input) to the full scale signal,
µ
expressed in dB. For example, if full scale is 1 V, then a dynamic reserve of 60 dB
µ
means noise as large as 1 mV (1000 times greater than 1 V) can be tolerated at the input
without overload.
Unfortunately, the word 'tolerable' allows some latitude in usage. Even without causing
overloads, large interfering signals can cause distortion and DC output errors in analog
components that can affect the measurement. For this discussion, dynamic reserve is
defined as follows:
The dynamic reserve of a lock-in amplifier at a given full-scale input voltage is the ratio
(in dB) of the Largest Interfering Signal to the full-scale input voltage. The Largest
Interfering Signal is defined as the amplitude of the largest interfering signal (not at the
reference frequency) that can be applied to the input before the lock-in cannot measure a
signal with its specified accuracy.
While dynamic reserve is quoted as a single number, the actual reserve depends upon the
frequency of the interfering signal. The reason for this has to do with the fact that a lock-
in amplifier applies (1) gain and (2) bandwidth-narrowing to the input signal, and it does
so in several stages. Depending on their frequency, different interfering signals are
rejected at different points. An interfering signal several MHz from the reference produces
a mixer output at several MHz; this signal is rejected by the IF low-pass filter
immediately following the mixer. An interfering signal 50 kHz from the reference is
rejected by the anti-aliasing filter before the A-D converter (see the following section for
a detailed functional description). A close-by interfering signal is rejected by the time-
constant filters in the DSP. Note: What about an interfering signal at 6 Hz offset, when the
-1 ≅
time-constant is only 3 ms ? 3 ms corresponds to a bandwidth of about 330 s 50 Hz,
this signal is within the instrument bandwidth and by definition is not an interfering signal.

Wide and Close Reserves

The fact that gain and bandwidth-narrowing occur in several stages leads to the question
of how best to allocate the gain between the different stages. At one extreme, one could
imagine all the gain to be in the DSP (digital signal processor), which wins with regard to
dynamic reserve since interfering signals suffer no amplification and are least likely to
cause overloads or distortion. The drawback to this is that the signal could get lost in the
noise at the A-to-D converter or mixer. (In analog lock-ins, the DSP gain was replaced by
output DC gain, which caused substantial problems with DC offset and drift). The other
extreme is to put the maximum gain as close to the signal input as possible; this approach
wins on noise performance, but has poor dynamic reserve. Since the interfering signals see
lots of gain, a relatively small interfering signal could cause an overload.
SR844 RF Lock-In Amplifier