Front End Electronics Internal Noise Source Characterization

Transcription

1 Front End Electronics Internal Noise Source Characterization Joe Brendler and R.H. Tillman May 14, 2015 Contents 1 Introduction 2 2 System Model 2 3 Measurement Process G r Measurement S 2 Measurement S 1 Measurement Measurement Stability 5 5 Data Processing 6 6 Example Result 7 7 Appendix IntSourceCharFEERev3.m IntTimeCalc.m Virginia Tech. brendler@vt.edu Virginia Tech. hanktillman@vt.edu 1

2 1 Introduction The Front End Electronics (FEE) used in this interferometer 1 uses a 3-State switching scheme for calibration of system gain and noise temperature. The calibration procedure is described in [1]. The FEE uses an SM4 Noise Diode (SM4) as its internal noise source. For accurate calibration, the noise temperature of this source must be well known. This document provides a detailed description of the methodology used to measure the noise temperature of the SM4 Noise Diode on a given FEE. Section 2 presents the system model. Section 3 discusses the measurement process. Section 4 discusses measurement stability for a given integration time used. Section 5 explains the MATLAB script used to process the data. Section 6 presents the results of the measurements. 2 System Model The power measured by a spectrum analyzer is given by S = k(t DUT + T SA )B r (1) where k is Boltzmann s constant, T DUT is the noise temperature of the DUT, T SA is the noise temperature of the spectrum analyzer, and B r is the resolution bandwidth (spectrum analyzer setting). For this measurement, simply using the SM4 noise diode as the DUT does not work, because it s output is not strong enough to dominate over the noise floor of the spectrum analyzer, i.e. T SA >> T DUT. For this reason, gain must be added in front of the spectrum analyzer to make it more sensitive. This gain also adds additional noise to the measurement, which must be measured and removed to obtain the noise temperature of the SM4. For this reason this gain is referred to as the characterized receiver for this measurement. Figure 1 shows a block diagram of the system model for the test setup. Attenuators are used between each gain stage, because the following cascade analysis assumes that stages are impedance matched. The amplifiers used are not perfect devices, and therefore reflections arise between them. The attenuators mitigate the effects of this reflection by reducing the strength of the reflected signal, thus improving the impedance match. The noise diode is an even poorer match to 50Ω, so additional attenuation is used between it and the characterized receiver. With this model, the Power Spectral Density (PSD) measured by the spectrum analyzer is: S 1 = kg r (T ON + T r )B r (2) where k is Boltzmann s constant, gain Gr and noise temperatures T ON and T r are as shown in the block diagram, and B r is the resolution bandwidth. G r can be measured directly. T r can be measured by connecting a matched load to the input of the receiver chain (see Figure 2), measuring its PSD, and solving for T r given that S 2 = kg r (T 0 + T r )B r (3) where T 0 is the known ambient temperature. Figure 2 shows a block diagram of the test setup for the S 2 measurement. The 10 db attenuator and 50Ω resistor are assumed to be a matched load, thus the input temperature in this setup is the ambient temperature, T 0, which was measured to be approximately 296 K

3 Figure 1: Block diagram of the system model for the S 1 measurement Figure 2: Block diagram of the system model for the S 2 measurement 3 Measurement Process The high-level procedure for using the setup described in the previous section to obtain a measurement of T ON, the noise temperature of the SM4 Noise Diode, is as follows: ˆ Measure G r ˆ Measure S 2 and use (3) to solve for T r ˆ Measure S 1 and use (2) to solve for T ON The following sections describe in detail the process that was used to obtain the results presented in Section G r Measurement The G r measurement is done using the FSH3 spectrum analyzer in scalar tracking generator mode. The detector must be set to RMS (the default is Sample) for measurements to have uncertainty as low as desired for this work. The characterized receiver includes everything from the cable connecting the SM4 noise diode to the 20 db attenuator to the cable connecting the ZJL-3G to the FSH3 as shown in Figure 1. Therefore, these cables must be included in the G r gain measurement. First, set the span of the FSH3 to 100 MHz with a 50 MHz center frequency. Set the Resolution Bandwidth to 1 MHz and the Sweep Time to 1 second. Set the FSH3 to tracking generator by selecting Meas, Tracking Generator. Before proceeding, assure that the detector is set 3

4 to RMS. Then, calibrate by selecting Transmission Cal. The display will say to replace the DUT with a through connection. To calibrate the spectrum analyzer, connect a cable from the RF Generator Output directly to the RF Input with an appropriate adapter and select Continue. This will calibrate the FSH3 to remove the loss of the cable. Disconnect the cable from the RF Input and connect it through a 15 db attenuator to the input of the characterized receiver (the cable before the 20 db attenuator). The 15 db attenuator is to assure that the amplifiers operate in their linear region. Connect the output of the ZJL-3G to the FSH3 RF Input with another cable. Power on the amplifiers with appropriate DC supply levels. The gain should be approximately a constant 4.5 db above 10 MHz. Linearity can be confirmed by adding an additional attenuator and observing that the gain decreases by the loss of the attenuator. In order to obtain measurements with extremely low levels of uncertainty, which is desirable for this work, multiple sweeps must be averaged. The FSH View software package 2 is used to pull multiple sweeps from the FSH3 and save them on a computer as.csv files. Connect the spectrum analyzer to a computer running FSH View and select the Multiple Transfers button in the toolbar. Select a folder to save the files to, and select a filename. This information will be needed later for the MATLAB scripts that process the data. For the G r measurement, 30 sweeps were found to be sufficient. Going beyond that surpasses the limit of measurement stability explained in Section 4. Set 1 second between sweeps to assure that each file contains a completely independent sweep. The loss of the 15 db attenuator used to assure linearity must be measured and removed from the G r measurement. This is done by re-calibrating the FSH3 to remove the loss of both the cable attached to the RF Generator Out port AND the RF Input port, so that the attenuator can be inserted and measured directly. Use the same FSH View multiple file procedure to obtain 30 sweeps of the attenuator gain, which should be approximately -15 db across the whole spectrum. 3.2 S 2 Measurement The setup for the S 2 measurement is shown in Figure 2. The 50Ω resistor is implemented with a coaxial load, which can be found in the box of adapters. The same DC power supply settings as used in Section 3.1 must be used for the amplifiers. For both this measurement and S 1, the FSH3 must be set in Analyzer mode. The reference level should be set to -20 dbm with the same Span, Center Frequency, Resolution Bandwidth, and Sweep Time as in Section 3.1. When the characterized receiver is powered on, the noise floor of the FSH3 should visibly increase by an order of magnitude. This is the measurement to be recorded as S 2. The same procedure as in Section 3.1 should be used to obtain the data files from FSH View, except this time many more files are required. The signal levels for the power measurements S 2 and S 1 are significantly lower than that of the gain measurement, and therefore the signal has more uncertainty due to noise. The results shown later in this document used 4000 files, providing uncertainty much less than 1%. This many files requires about 2 and a half hours of recording. 3.3 S 1 Measurement The setup for the S 1 measurement is shown in Figure 1. The FEE must be biased in State 3 (requires a supply voltage > 20 V DC ) so that the noise diode is turned on. First, the characterized 2 Available at 4

5 Figure 3: Lab Bench Test Setup receiver should be powered on. The noise floor should jump as before. Then, the FEE should be powered on and biased to State 3. The signal on the FSH3 should then jump another order of magnitude from the addition of the noise from the SM4 noise diode. The rest of the data collection procedure is the same as with the S 2 measurement. For the S 1 measurement, a temperature data logger should be used to measure the ambient temperature next to the noise diode on the FEE. This device can be configured using OnSet s HoboWare software 3. Figure 3 shows a picture of the test setup on the lab bench with the characterized receiver connected to the spectrum analyzer as in the S 1 and S 2 measurements. The input to the receiver is shown unconnected. This would be connected to the SM4 Noise Diode for S 1 measurements, and to the matched load for S 2 measurements. 4 Measurement Stability This section explains the importance of selecting an appropriate number of files to save for averaging for each measurement. For the final T ON measurement, it is desirable to obtain much less than 1% uncertainty (± 0.5%) between the measurement and a polynomial fit. That requires a certain integration time for each measurement used to compute T ON, such that each individual measurement s own uncertainty is much less than 1%. In Analyzer Mode using the RMS Detector, the FSH3 measures the PSD of a signal at 301 points across the spectrum. The integration time per point per sweep is therefore given by Sweep Time/301 seconds. The variance between a measurement and its polynomial fit decreases as integration time increases. There is a limit to that improvement in variance due to digitizing hardware. The integration time used should come before that limit so that measurements are limited by noise in the analog system and not the digitizer. The spectrum analyzer was set up to continuously create data files to be averaged, each containing a one second sweep, or 1/301 s of integration. This method was used to measure S 2. Figure 4 shows a plot of the variance of the measurement vs. the 3 Available at 5

6 Figure 4: Plot of variance vs. integration time for the S 2 measurement. integration time. The variance is shown to continue decreasing as integration time increases, meaning the limit has not been reached. For this reason, longer measurements could be still be taken to reduce error if deemed necessary. 5 Data Processing The MATLAB script, IntSourceCharFeeRev3.m (included in the Appendix in Section 7) can be used to produce plots of all the measurements made in this process along with polynomial fits and percent error bars to show the uncertainty of the measurements. It has a few constants that must be set each time the script is used. The resolution bandwidth variables BrS2 and BrS1 must be set to the resolution bandwidths used for the S 2 and S 1 measurements, respectively. Based on the directions given above, these should be set to 1e6 for 1 MHz RBW. If the RBW ever changes for future measurements, these variables must be changed accordingly. The variable polyfitorder, which sets the order of the polynomial fit to the curves is currently set to 27, but should be changed if the measurements appear to require a different order polynomial (discussed further at the end of this section). Under the Parse Data cell, the same directory and filename as used in the FSH View multiple file procedure should be set for each measurement 4. These measurements, in order, are S 2, S 1, G r, and the measured 15 db attenuator. The following is a summary of what the IntSourceCharFeeRev3.m script does ˆ Each measurement is parsed so that the columns (power or gain) are placed into an array where rows correspond to frequency points and each column is one 1 second sweep. 4 The files will actually have longer names than written under filename that include timestamps, but this script only requires that the given filename be used. 6

7 Figure 5: Plot of the S 2 measurement ˆ The span is truncated to MHz, the frequency range of interest for this work. All of the data is recorded in db scale, so it is converted to linear units to work with the equations presented above. ˆ All of the columns are averaged into one column that contains the mean of all sweeps. ˆ The attenuator gain is removed from the G r measurement, and T r and T ON are computed using (3) and (2). ˆ A polynomial is fit to each measurement. ˆ Plots of each measurement with the polynomial fit are produced, showing both the actual measurement and the percent error for the measurement. The variance vs. integration time plot shown in Figure 4 was obtained using the IntTime- Calc.m MATLAB script (included in the Appendix in Section 7). The same procedure is used to give the script the relevant filename and directory as with the IntSourceCharFeeRev3.m script, as well as setting the order of the polynomial fit. This script should be used for each measurement to show that the measurement has not been limited by the digitizing hardware of the FSH3. It also shows a plot of the measurement with its polynomial fit, which is useful to assure that the order of polynomial chosen is appropriate. 6 Example Result Figures 5 through 11 show example results for one run of the procedure described in this document. 7

8 Figure 6: Plot of the S 1 measurement Figure 7: Plot of the G r measurement without the attenuation removed. 8

9 Figure 8: Plot of the measured attenuation used to assure the characterized receiver operated linearly during the G r measurement. Figure 9: Plot of the G r measurement with the attenuation removed. 9

10 Figure 10: Plot of the receiver noise temperature, T r. Figure 11: Plot of the SM4 Noise Diode temperature, T ON. 10

11 References [1] R. Tillman, Design and Evaluation of a HELA-10 Based FEE with 3-State Switched Calibration, Virginia Tech, Available: Tech. Rep., April 2013, [Online]. 7 Appendix 7.1 IntSourceCharFEERev3.m Following this page is the IntSourceCharFEERev3.m MATLAB script described in this document. 11

12 % Filename : IntSourceCharFEErev3.m % Author : Joe Brendler % Date Created : February 4, 2015 % Description : Produces a plot of a set of measurements as well as the % + or - 1% uncertainty limits for the average of the set. Used to confirm % individual measurements are within 1% uncertainty of the average of the % dataset. Used to characterize the internal noise source for FEE rev 3.0 % % ======================================================================= % close all; clear all; warning('off','matlab:axes:negativedatainlogaxis'); figindex = 1; BrS2 = 1e6; BrS1 = 1e6; k = *(10^(-23)); To = 296; polyfitorder = 27; % Resolution Bandwidth [Hz] for S2 measurement % Resolution Bandwidth [Hz] for S1 measurement % Boltzmann's Constant % Ambient Temperature [K] % Order of the polynomial fit to the result %% Parse Data directory = 'C:\Users\Joe\Documents\MATLAB\FSHMultiSweeps\150422_S2_NewRx'; % S2 file directory filenames2 = 'S2'; [freq, DATAS2, filelists2] = FSHMultiFiles(filenameS2, directory, 34, 334); % S2 files directory = 'C:\Users\Joe\Documents\MATLAB\FSHMultiSweeps\150422_S1_NewRx'; % S1 file directory filenames1 = 'S1'; [freq, DATAS1, filelists1] = FSHMultiFiles(filenameS1, directory, 34, 334); % S1 files directory = 'C:\Users\Joe\Documents\MATLAB\FSHMultiSweeps\150507_Gr_NewRx'; % Gr file directory filenamegr = 'Gr'; [freq, DATAGr, filelistgr] = FSHMultiFiles(filenameGr, directory, 33, 333); % Gr files directory = 'C:\Users\Joe\Documents\MATLAB\FSHMultiSweeps\150403_attn'; % attn file directory filenameattn = 'attn'; [freq, DATAattn, filelistattn] = FSHMultiFiles(filenameattn, directory, 33, 333); % attn files freq = freq(91:241,1); freq = freq.*10^-6; % Frequency axis in MHz from MHz %% Parse ARX Data %% Convert to Linear Units 12

13 DATAS2 = 10.^(DATAS2./10)*.001; DATAS1 = 10.^(DATAS1./10)*.001; DATAGr = 10.^(DATAGr./10); DATAattn = 10.^(DATAattn./10); % From dbm % From db %% Compute Mean S2 Curve MeanS2 = mean(datas2(91:241,1:(length(datas2(1,:)))),2); files % Mean of all S2 %% Compute Mean S1 Curve MeanS1 = mean(datas1(91:241,1:(length(datas1(1,:)))),2); files % Mean of all S1 %% Compute Mean Gr Curve MeanGr = mean(datagr(91:241,1:(length(datagr(1,:)))),2); files % Mean of all Gr %% Compute Mean attn Curve Meanattn = mean(dataattn(91:241,1:(length(dataattn(1,:)))),2); all attn files % Mean of %% Remove attenuation from Gr Gr_attn_removed = MeanGr./Meanattn; %% Noise Temp Computation % Tr Tr = (MeanS2./(k.*Gr_attn_removed.*BrS2)) - To; % Ton Ton = (MeanS1./(k.*Gr_attn_removed.*BrS1)) - Tr; %% Polynomial Fit for Ton pton = polyfit(freq, Ton, polyfitorder); Ton fit_ton = polyval(pton, freq); varhighton = fit_ton + abs(0.005.*fit_ton); varlowton = fit_ton - abs(0.005.*fit_ton); % Polynomial coefficients for % Polynomial fit to Ton % High 1% uncertainty limit % Low 1% uncertainty limit %% Polynomial Fit for Tr ptr = polyfit(freq, Tr, polyfitorder); fit_tr = polyval(ptr, freq); varhightr = fit_tr + abs(0.005.*fit_tr); % Polynomial coefficients for Tr % Polynomial fit to Tr % High 1% uncertainty limit 13

14 varlowtr = fit_tr - abs(0.005.*fit_tr); % Low 1% uncertainty limit %% Polynomial Fit for Gr (including attn) pgr = polyfit(freq, MeanGr, polyfitorder); fit_gr = polyval(pgr, freq); varhighgr = fit_gr + abs(0.005.*fit_gr); varlowgr = fit_gr - abs(0.005.*fit_gr); % Polynomial fit to Gr % High 1% uncertainty limit % Low 1% uncertainty limit %% Polynomial Fit for Gr (NOT including attn) pgr_attn_removed = polyfit(freq, Gr_attn_removed, polyfitorder); % Polynomial coefficients for Gr fit_attn_removed = polyval(pgr_attn_removed, freq); % Polynomial fit to Gr varhighgr_zfl = fit_attn_removed + abs(0.005.*fit_attn_removed); 1% uncertainty limit varlowgr_zfl = fit_attn_removed - abs(0.005.*fit_attn_removed); 1% uncertainty limit % High % Low %% Polynomial Fit for attn pattn = polyfit(freq, Meanattn, polyfitorder); for Gr fit_attn = polyval(pattn, freq); varhighattn = fit_attn + abs(0.005.*fit_attn); limit varlowattn = fit_attn - abs(0.005.*fit_attn); limit % Polynomial coefficients % Polynomial fit to Gr % High 1% uncertainty % Low 1% uncertainty %% Polynomial Fit for S1 ps1 = polyfit(freq, MeanS1, polyfitorder); Gr fit_s1 = polyval(ps1, freq); varhighs1 = fit_s1 + abs(0.005.*fit_s1); varlows1 = fit_s1 - abs(0.005.*fit_s1); % Polynomial coefficients for % Polynomial fit to Gr % High 1% uncertainty limit % Low 1% uncertainty limit %% Polynomial Fit for S2 ps2 = polyfit(freq, MeanS2, polyfitorder); Gr fit_s2 = polyval(ps2, freq); varhighs2 = fit_s2 + abs(0.005.*fit_s2); varlows2 = fit_s2 - abs(0.005.*fit_s2); % Polynomial coefficients for % Polynomial fit to Gr % High 1% uncertainty limit % Low 1% uncertainty limit %% PSD Plot S1 14

15 figure(figindex); subplot(2,1,1); h1_s1 = plot(freq,varhighs1,'--r',freq,varlows1,'--r',freq,means1,'-b'); % Plots the + or - 1% uncertainty limits h2_s1 = plot(freq, fit_s1, '--g'); ylabel('s1 (W/RBW)'); legend([h1_s1(3) h2_s1],{'mean', 'Fit'}); pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(MeanS1 - fit_s1)./fit_s1, freq, pererrhigh, '--r', freq, pererrlow, '--r'); ylabel('percent Error (%)'); figindex = figindex + 1; %% PSD Plot S2 figure(figindex); subplot(2,1,1); h1_s2 = plot(freq,varhighs2,'--r',freq,varlows2,'--r',freq,means2,'-b'); % Plots the + or - 1% uncertainty limits h2_s2 = plot(freq, fit_s2, '--g'); ylabel('s2 (W/RBW)'); legend([h1_s2(3) h2_s2],{'mean', 'Fit'}); pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(MeanS2 - fit_s2)./fit_s2, freq, pererrhigh, '--r', freq, pererrlow, '--r'); ylabel('percent Error (%)'); figindex = figindex + 1; %% Receiver Gain Plot Gr (including attn) figure(figindex); subplot(2,1,1); h1_gr = plot(freq,varhighgr,'--r',freq,varlowgr,'--r',freq,meangr,'-b'); % Plots the + or - 1% uncertainty limits 15

16 h2_gr = plot(freq, fit_gr, '--g'); ylabel('receiver Gain Gr'); legend([h1_gr(3) h2_gr],{'mean', 'Fit'}); pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(MeanGr - fit_gr)./fit_gr); ylabel('percent Error (%)'); figindex = figindex + 1; %% Receiver Gain Plot Gr (NOT including attn) figure(figindex); subplot(2,1,1); h1_gr = plot(freq,varhighgr_zfl,'--r',freq,varlowgr_zfl,'-- r',freq,gr_attn_removed,'-b'); % Plots the + or - 1% uncertainty limits h2_gr = plot(freq, fit_attn_removed, '--g'); ylabel('gr (attenuation removed)'); legend([h1_gr(3) h2_gr],{'mean', 'Fit'}); pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(Gr_attn_removed - fit_attn_removed)./fit_attn_removed); ylabel('percent Error (%)'); figindex = figindex + 1; %% Attenuator Plot for Attn used to measure Gr figure(figindex); subplot(2,1,1); h1_attn = plot(freq,varhighattn,'--r',freq,varlowattn,'--r',freq,meanattn,'- b'); % Plots the + or - 1% uncertainty limits h2_attn = plot(freq, fit_attn, '--g'); ylabel('attenuator Gain'); legend([h1_attn(3) h2_attn],{'mean', 'Fit'}); 16

17 pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(Meanattn - fit_attn)./fit_attn); ylabel('percent Error (%)'); figindex = figindex + 1; %% Noise Temp Plot Tr figure(figindex); subplot(2,1,1); h1_tr = plot(freq,varhightr,'--r',freq,varlowtr,'--r',freq,tr,'-b'); % Plots the + or - 1% uncertainty limits h2_tr = plot(freq, fit_tr, '--g'); ylabel('receiver Noise Temperature (K)'); legend([h1_tr(3) h2_tr],{'t_r', 'Fit'}); pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(Tr - fit_tr)./fit_tr, freq, pererrhigh, '--r', freq, pererrlow, '--r'); ylabel('percent Error (%)'); figindex = figindex + 1; %% Noise Temp Plot Ton figure(figindex); semilogy(freq, Ton, freq, fit_ton); ylabel('noise Temperature (K)'); legend('t_o_n', 'Fit'); figindex = figindex + 1; %% Polyfit Plot Ton figure(figindex); subplot(2,1,1); 17

18 h1_ton = plot(freq,varhighton,'--r',freq,varlowton,'--r',freq,ton,'-b'); % Plots the + or - 1% uncertainty limits h2_ton = plot(freq, fit_ton, '--g'); ylabel('noise Diode Noise Temperature (K)'); legend([h1_ton(3) h2_ton],{'t_o_n', 'Fit'}); pererrhigh(1:length(freq)) = 0.5; pererrlow(1:length(freq)) = -0.5; subplot(2,1,2); plot(freq, 100.*(Ton - fit_ton)./fit_ton, freq, pererrhigh, '--r', freq, pererrlow, '--r'); ylabel('percent Error (%)'); figindex = figindex + 1; 18

19 7.2 IntTimeCalc.m Following this page is the IntTimeCalc.m MATLAB script described in this document. 19

20 % Filename : IntTimeCalc.m % Author : Joe Brendler % Date Created : January 29, 2014 % Description : Produces a plot of mean-squared error vs. integration % time for spectrum analyzer measurements. Can be used to determine the % point at which further increasing the integration time no longer improves % the variance in a measurement. % % ======================================================================= % close all; clear all; warning('off','matlab:axes:negativedatainlogaxis'); polyfitorder = 27; % Order of the polynomial fit to the result %% Parse Data directory = 'C:\Users\Joe\Documents\MATLAB\FSHMultiSweeps\150422_S2_NewRX'; % Files' Directory filename = 'S2'; [freq, DATA, filelist] = FSHMultiFiles(filename, directory, 34, 334); % Parse data from the sweeps freq = freq(91:241,1); freq = freq.*10^-6; % Frequency axis in MHz from MHz AVG = zeros(length(freq), length(filelist)); matrix holding averages from MHz % preallocate array size for DATA = 10.^(DATA./10); %% Polynomial fit to total average TotalMean = mean(data(91:241,1:(length(data(1,:)))),2); % Mean of all files p = polyfit(freq, TotalMean, polyfitorder); % Polynomial coefficients for MHz fit = polyval(p, freq); % Polynomial fit to the curve %% Compute Averages numaverages = 1; % Start by averaging each file together to make a point % on the plot. Then once the next decade is reached, % average 10 files, 100 for the next decade, and so % on, to evenly distribute points throughout the plot. % Generates a matrix where each column is the average of "i" (number of columns) data % files. count = 1; for i = 1:(length(DATA(1,:))) 20

21 AVG(:,i) = mean(data(91:241,1:i),2); % Returns one column that contains the average % for MHz of i columns % Compute variance and integration time if mod(i,numaverages) == 0 % Compute Variance Var(count) = sum((avg(:,i) - fit).^2)/(i); % Variance b/w curve & fit % Var(count) = var(avg(:,i) - fit); % Using MATLAB's variance function % Compute Integration Time Tau(count) = i*( *10^(-3)); % 3.32 ms/pixel per second, 1s sweep per file % If the current value of tau is in the next decade, multiply the % spacing between points by 10 (to get evenly distributed points) if count == 1 currentdecade = log10(tau(count)); else if log10(tau(count)) >= (currentdecade+1) numaverages = numaverages*10; currentdecade = currentdecade + 1; end end end end count = count + 1; %% Plotting loglog(tau, Var, '-x'); xlabel('integration Time (s)'); ylabel('variance'); %% Polyfit Test % plot of polyfit test. figure(2); plot(freq, TotalMean, freq, fit); ylabel('power [arb db]'); legend('measurement', 'Polyfit'); 21