Gentec-EO T-Rad-USB (LEMO) - Manual (Page 6)

T-RAD-LEMO-USB Instruction Manual Version 2.0 June 2012 6
If we set B to unity and hold it constant, then the result is a signal that is:
1. Proportional to the A, the amplitude of the input signal.
2. Proportional to the cosine of the phase angle between the two signals.
3. Modulated at two times the input signal frequency.
If we set the phase difference to zero degrees then the resulting signal can be passed through a
low pass filter with a time constant of tau and the result will be:
This shows that once the filter has settled, the signal is a DC representation of the original input. We can
now set the filter time constant as high as needed to block out unwanted noise and interference. The
details of how the lock in implements this math can be found in the literature.
One subject of interest arises from the requirement to set the phase difference to zero degrees. In
practice, the phase difference is not known. Since the cosine function returns values between one and
negative one as the phase is changed, the phase is simply adjusted until the signal maximizes. It is
actually easier to adjust the phase until the signal goes to zero and then shift the phase by 90 degrees. If
the signal goes negative, shift the phase 180 degrees. The signal will now be maximized.
If this seems like a bother, it is. The Gentec-EO Lock In Amplifier uses a dual phase approach which
relieves the user of the need to adjust the phase. A sine wave signal is generated by the instrument at the
reference frequency, and at the reference frequency plus 90 degrees, or pi divided by 2. The input signal
is multiplied by both reference signals. The results of those multiplications are then squared, summed,
and the square root is taken. Look at the final equation for the output after the multiplication, ignoring the
second term:
The output of the second multiplication will be: