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Why we want to do this

Simply because we can tell an awful lot about a bolometer if we can measure its full complex impedance. On our Twiki Library page you can find a link to a paper by John Vaillancourt (or go here) where he goes through some of the things you can learn about using complex impedance.

Long story short: When you measure Z(w) for a bare bolometer it will trace a semi-circle in the complex plane. That semi-circle gives information that can be combined with independent resistance and I-V measurements to characterize the full complex impedance, time constants, sensitivities, heat capacitances, and thermal conductances. That's a lot of information and all of it should be available through measurements with the DfMUX.

Short outline of the process

Step by step process for data taking:

1. Lower bolometers into transition.
2. Do not null the carrier (this would affect the phase of the recovered carrier and we don't want to do that.)
3. Set FIR stage. (the default is FIR5, but set this lower to FIR3 while streaming data.)
4. Set up 'helper'
   1. set the amplitude of the helper to 0.001
   2. set the frequency of the helper to f_carrier + delta. (delta is the desired frequency separation between the carrier and helper.)
   3. set the frequency of the helper's demodulator to f_carrier - delta - 24
5. Stream data
6. Repeat steps 4 and 5 for each delta.
7. Write data to file. (data is saved in a dictionary in a pickle file. Each entry is a data stream.)
8. Reset to FIR5.

Step by step process for analysis

1. Load data from the pickle file.
2. Determine the frequencies at which signals should appear. (minus side band [msb] at 24 Hz, carrier [car] at 24 + delta, (helper + plus side band [psb]) [hel] at 24 + 2*delta)
3. Using the sampling rate create a 'time stamp' with same sampling rate
4. create basis functions for fitting the msb, car and hel (create 7 functions that are sampled at the time stamp's entries)
   1. sine and cosine with frequency = 24 Hz
   2. sine and cosine with frequency = 24 + delta Hz
   3. sine and cosine with frequency = 24 + 2*delta Hz
   4. DC level
5. Construct matrix of basis functions (B)
6. Calculate the coefficients for each of the basis functions C = (B*B.T).I*B*a.T
7. Use the coefficients to create the fitted msb, car and hel
8. mix (msb x car = msb_m) and (hel x car = hel_m)
9. create basis functions for the low frequency terms of the mixing
   1. sine and cosine with frequency = delta
10. construct matrix of basis functions (B2)
11. fit for the low frequency terms of mixing
    1. C_msb = (B2*B2.T).I*B2*msb_m.T
    2. C_hel = (B2*B2.T).I*B2*hel_m.T
12. Use knowledge that psb = msb* to say that A_sine_psb = -A_sine_msb and A_cosine_psb = A_cosine_msb
13. Separate psb from the helper. A_sine_helper = A_sine_hel - A_sine_psb = A_sine_hel + A_sine_msb; A_cosine_helper = A_cosine_hel - A_cosine_psb = A_cosine_hel - A_cosine_msb
14. Use the coefficients for the sine and cosine components to calculate the phase of mixed psb and helper.
    1. phase_psb = arctan(-A_sine_msb, A_cosine_msb)
    2. phase_helper = arctan(A_sine_hel + A_sine_msb, A_cosine_hel - A_cosine_msb)
15. Subtract phases to find phase shift

Well below the 3dB point the relative phase of the psb and helper should be constant. As delta moves through the bolometer time constant the relative phase between the psb and helper should move to 90 degrees lower.

-- PeterHyland - 20 Apr 2009

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This topic: BolometerTesting > WebHome > ComplexImpedance Topic revision: r12 - 2009-09-18 - PeterHyland

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