Units; Rms Or Peak; Degrees Or Radians - Stanford Research Systems SR844 User Manual

2-4 SR844 Basics
which is proportional to the cosine of the phase difference between the input and the
reference. Hence the term phase sensitive detection.
In order to measure V
reference,
mixers, with the reference inputs 90
mixer is V
V
M2
After filtering,
V
M2+FILT
The amplitude and phase of the input signal can be determined from the two mixer
outputs, Eqn (2-3) and (2-6). These computations are handled by the DSP chip in the
SR844.
Amplitude
Phase
In-Phase
Component
Quadrature
Component

Units

RMS or Peak ?

Lock-in amplifiers as a general rule measure the input signal in Volts rms. When the
SR844 displays a magnitude of 1 V (rms), the sine component of the input signal at the
reference frequency has an amplitude of 1 Vrms or 2.8 Vpk-pk. This is important to
remember whenever the input signal is not a sine wave. For example, if the signal input is
a square wave with a 1 Vpk (2 Vpk-pk) amplitude, the sine component at the fundamental
frequency has a peak amplitude of 4/
√
(Vpk/ 2) or 0.9 Vrms.

Degrees or Radians ?

In this discussion, frequencies have been referred to as f [Hz] and ω [radian/sec].
ω = 2πf
This is because it is customary to measure frequency in Hertz, while the math is most
convenient using
and MHz. The equations used to explain the calculations are often written using
simplify the expressions.
SR844 RF Lock-In Amplifier
using Eqn (2-3), the phase difference between the signal and
I
θ θ
– , must be stable and known. The SR844 solves this problem by using two
R I
ω θ π
sin( t+ – /2) and the output of the second mixer is
R R R
=
½ V V cos(θ –θ –π/2) + ½ V
I R R I
=
½ V V cos(θ –θ –π/2)
I R R I
=
½ V V sin(θ –θ )
I R R I
R =
(2/V
θ
= tan
–θ
R I
X =
R cos (θ
Y = R sin (θ
ω
. For purposes of measurement, the SR844 reports frequency in kHz
°
out of phase. The reference input to the second
V sin(2ω t+θ
I R R
) × √[ (V
2
) + (V
R M1+FILT
-1
(V /V )
M2+FILT M1+FILT
–θ )
R I
–θ )
R I
π ×
1 Vpk. The lock-in displays the rms amplitude
(2-4)
+θ –π/2)
R I
(2-5)
(2-6)
2
(2-7)
) ]
M2+FILT
(2-8)
(2-9)
(2-10)
(2-19)
ω
to