1. Calculation of the phases of injected pulsars from the servo loop
X. Siemens, B. Allen, M. Landry
LIGO-G Z
The phases of the injections can be determined from the functions that make up the servo loop

2. Servo loop with injection points
The actuation function:
negative
During S2 the pulsar signals were injected into M.
During S3 into L.

3. If we ignore contributions from external noise and go around the loop:
Injection point M is the simplest because injected signals are seen by entire actuation.
If we ignore contributions from external noise and go around the loop:
Expect phase of injected signal to be shifted by the phase of the actuation function as well as an overall factor of
h=Calibrated AS_Q
Expected signal

4. Injection point L is more involved because injected signals see only part of the actuation function.
Once again we ignore contributions from external noise and go around the loop:
Also expect phase of injected signal to be shifted by the phase of the actuation function as well as an overall factor of !
Calibrated AS_Q
Expected signal

5. Some results S2: S3: Strongest Weakest expected (measured) Signal 1H1
102o (100o)
102o (98o) H2
100o (98o)
99o (100o) L1
94o(84o +/- 15o)
93o (86o+/-10o)
S3:
expected (measured)
Pulsar 4
Pulsar 3
Pulsar 2
Pulsar 1
Pulsar 0 H1
108o (105o)
302o (303o)
164o (105o)
338o (354o)
112o (126o) H2
100o (102o)
303o (301o)
163o (122o)
331o (312o)
117o (234o) L1
279o (98o)
122o (276o)
240o (117o)
151o (144o)
52o (---)
Strongest Weakest

6. Conclusions
We can predict phases of injected CW signals as seen in a calibrated AS_Q from models of the servo loop.
We know how to account for actuation in future injections.
- Injection phases of pulsars agree well with prediction for S2 and S3 (except for L1) … Problem with calibration functions?