[Zach, Koji]
Last week, we did some work towards calibrating the actuation gains of the VCO and NPRO PZT, which was documented in Koji's elog posts. This post summarizes the method.
First, a sine wave with a nominal amplitude of 10 mVpp @ 1 kHz was injected into the PZT sweep of the primary PDH box, and the peaks in the primary error and feedback signals were recorded, as well as that in the secondary error signal (which was being held in the linear response region by the main servo):
- Primary error:
**685.2410 uVrms**
- Primary feedback:
**98.7438 uVrms**
- Secondary error:
**64.9701 uVrms**
Note that the error signals were being read out at INMON, so they are multiplied up by ~42.
Next, the same drive signal was connected to the Tektronix VCO external FM input, with a nominal deviation setting of 100 kHz/V and a carrier frequency of 47.5 MHz (as usual). The output was then connected to the RF analyzer to study its frequency structure and determine the modulation depth.
The structure of an FM signal in frequency space consists of a carrier and a series of sidebands at integer numbers of the modulation frequency from the carrier, whose powers are determined by the bessel expansion. I.e., the nth sideband will be at a frequency f_{c} + n*f_{mod} with a power P_{n} = ( J_{n}(Γ)/J_{0}(Γ) )^{2} * P_{c}, where Γ = Δf / f_{mod} is the modulation depth and 2*Δf is the peak-to-peak amplitude of the frequency modulation.
The powers of the sidebands were measured (in dBm) and divided by the carrier power, and this array of values was fit to the appropriate array of bessel function ratios to obtain a modulation index and therefore an FM amplitude. Below are two plots, one for the 1-kHz excitation mentioned above and another for the same test done with a 100-Hz excitation with the same amplitude, which is more impressive and used more points.
The inferred peak-to-peak FM deviation was thus ~993 * 2 = 1986 Hz. Since the FG displays the voltage for a 50-ohm load, this value is reasonable as the external FM input has an impedance of 10kohm. So, 0.01 mVpp (*2 for display error) * 10K/(10K + 50) * 100 kHz/V ~ 1990 Hzpp.
This signal was put into the AOM and elicited a peak of **247.258 Vrms **in the secondary loop error signal. Since the AOM is double passed, the true optical deviation was 2 * 1986 = 3972 Hzpp. This implies that, when it was put into the PZT sweep input, the same injection caused a deviation
(64.9701 uVrms / 247.258 uVrms) * 3972 Hzpp = 1043 Hzpp.
Using the signal strength in the PZT feedback path from above, we can infer a PZT actuation gain of
G_{PZT} = 1043 Hzpp / (98.7438 uVrms * 2*sqrt(2)) = **3.734 MHz/V** |