13.0 Waveform Receiver (WFR)

13.1 WFR Subsystem Description

This section of the RPWS Calibration Document describes the five-channel Waveform Receiver (WFR), extending the description contained in the Section 3 instrument overview. The WFR subsystem provides simultaneous measurements of plasma wave signals from up to five separate sensors. The purpose of this receiver is to provide high resolution spectral measurements down to 1 Hz and to provide simultaneous waveform information from five sensors for the purpose of determining the polarization and propagation vector of the low frequency plasma waves and radio emissions. When utilizing the Langmuir Probes, the WFR can provide n/n waveforms, including time delay measurements between the different sensors. During data analysis on the ground, signal processing routines will analyze the five-component measurements, providing cross-correlation products which may be used to deduce the wave normal, Poynting, and polarization vectors. The WFR is similar to waveform receivers previously designed for the Polar spacecraft.

13.2.1 General WFR Characteristics

The WFR consists of five parallel analog input channels, with each channel dedicated to an electric, magnetic, and/or a Langmuir sensor. The five channel inputs are coupled directly to the differential amplifiers of the electric antennas [EXLO (dipole) and EZLO(monopole)], the magnetic search coil antennas (BX, BY, and BZ), and Langmuir Probe (LMR+, LMR-, and LMR). It should be noted that the HFR can provide to the EXLO input of the WFR either the Ex+ or Ex- monopole electric antenna, and that the LMR+ and LMR- are the Ex+ and Ex- antenna elements used as a Langmuir Probe. The first channel of the WFR can select between EXLO and LMR+; the second can select between EZLO and LMR-; the third can select between BX and LMR; and the fourth and fifth are always connected to the BY and BZ, respectively. Signals from the five antennas are routed directly to a gain select stage which provides commandable gains of 0, 10, 20, or 30 dB for each receiver channel. The first two channels have independent gain settings, but the last three channels share the same gain control lines. The gain increments are provided by programmable gain amplifiers which are similar to those used for gain control in the WBR. During operations, the gain state for each receiver channel is selected by the HRP in response to appropriate spacecraft commands. The output of the programmable gain amplifiers goes to a 27 Hz lowpass filter and a 3 Hz to 2.5 kHz bandpass filter (a 3 Hz highpass filter and a 2.5 kHz lowpass filter). The desired frequency range sent to the A/D driver is selected by spacecraft command. The output from the A/D driver goes to the HRP. On the HRP, the signals are then sampled simultaneously by sample-and-hold circuits and routed to multiplexers to 12-bit analog to-digital converters. The WFR can also be commanded to measure one, two, three or four channels. These special modes allow greater resolution for special observations. The WFR provides the Low-Frequency Digital Receiver (LFDR) one or two channels of low frequency (1 to 27 Hz) data.

13.1.2 Frequency Response

The frequency response of the WFR is determined by the low frequency cutoff of the sensor's differential amplifiers ( 1 Hz), and by the filters which follow the gain control stage of each of the five receiver channels. The 2.5 kHz lowpass filters are of the passive type, but the 27 Hz lowpass filters and the 3 Hz highpass fitters are active. The bandwidth of the WFR is selected by the HRP (WFRBND command) in response to the appropriate spacecraft command. Listed below are the filter commands:

Back End Filter	WFRBND	Sampling Rate

27 Hz LPF	1	10 ms

3 Hz - 2.5 kHz	0	140 s

13.1.3 Phase Response

Since the primary purpose of the WFR is to provide cross-correlations between the five measured wave components, each receiver channel must have a known phase response. To this purpose, it is specified that all five lowpass passive filters are matched in phase response, and are determined to be phase-stable within a 1% ( 3°) margin within 1 Hz to 2.5 kHz.

13.1.4 Gain Select

The gain select stage of each channel of the WFR employs a variable gain amplifier which may be selected to provide gains of 0, 10, 20, and 30 dB. The first two channels have independent gain settings, but the last three channels share the same gain control lines. The gain is selected by the HPR (WFG command) in response to the appropriate spacecraft command.

13.1.5 Receiver Inputs

The selection of the sensor signal inputs for the first three channels of the WFR is determined by the HRP (WFRSEN command) in response to the appropriate spacecraft command. The WFR will have the capability of processing signals from the following sensors:

Command Setting Sensor Channel

WFRSEN0	0	LMR+	0

WFRSEN0	1	EXLO	0

WFRSEN1	0	LMR-	1

WFRSEN1	1	EZLO	1

WFRSEN2	0	BX	2

WFRSEN2	1	LMR	2

BY	3

BZ	4

13.1.6 Power

The WFR is provided with four power supply lines. The regulated supply voltages and expected average current loads are as followed:

+12 V	3.6 mA

−12 V	3.8 mA

+ 6 V	28 mA

− 6 V	34 mA

The total power requirement for the WFR is expected to be 461 mW.

413.1.7 Receiver Output

The output signal from the WFR A/D drivers goes to the HRP to be processed before being transmitted to the ground. See the Data Processing Unit sections for a detailed discussion of this processing.

13.2.1 Conversion of Data Numbers to Science Units

This section describes the procedure for obtaining a calibrated data value from a WFR raw measurement.

1. First a snapshot consisting of 2N raw WFR data samples is obtained. These data samples are 12-bit unsigned values (0-4095).

2. The DC component is obtained by averaging the 2N samples. The DC component is subtracted from the 2N samples, because the receiver is an AC coupled system and the DC component is not related to any sensor measurement. Furthermore, removal of the DC offset is needed for the next step.

3. The proper counts-to-volts rms factor is now applied to the data. This is the amplitude in counts of a sine wave in the middle of the pass-band which would be measured by the WFR if a 1 volt rms signal were injected into the Ex antenna inputs and the WFR had no gain amplifiers turned on. The 2N samples are all divided by this factor. Throughtout the calibrations, another way this is expressed is the decibels below a maximum sine wave; for 12 bit data, which can range from 0 to 4095, this is dB below a sine wave amplitude of 2047.5 counts ( or 4095 counts peak-to-peak ) and it is referred to as dB max. This factor depends upon the filter mode and gain. The conversion factors are given in section 13.3.2 in tables 13.3.2.1 and 13.3.2.2.

4. Next the WFR gain amplifier value must be divided out. The gain can vary from 0 dB through 30 dB in steps of 10 dB. If the gain is G, then the 2N samples should all be divided by 10G/20.

5. Next a Hanning window can be applied to the 2N samples. For a Hanning window the coherent gain is 0.5 ( see "Digital Filter Design Handbook" by Fred J. Taylor). Therefore the 2N samples must then be multiplied by 2. The equation for a Hanning window is Hi = 0.5*(1-cos(2* *i/(2N -1))) for i = 0, 2N -1.

6. A FFT should be performed on the 2N samples. The FFT output must be normalized using whatever normalization factors are necessary to give the amplitude of a sine wave when real and imaginary parts are squared, summed and the square root is taken. The normalization factors may be different for different FFT implementations. The phase information for the FFT is not useful, so the magnitudes can now be calculated by squaring the real and imaginary parts, summing and then taking the square root. This yields volts rms in each FFT bin. This is the voltage difference Vdiff betweeen the Ex+ and Ex- antennas at the frequency corresponding to that FFT bin.

7. Once the voltage Vdiff is found, the sensor-dependent conversion factor must be used to adjust the voltage. The voltage difference between the Ex+ and Ex- antennas is given the symbol VDEx. Since the voltage difference Vdiff calculated in steps 1 through 6 is for the voltage difference between the Ex+ and Ex- antennas, no conversion is necessary for VDEx. VDEx is equal to Vdiff. The voltage between the Ez antenna and spacecraft ground is given the symbol VEz. The voltages at the outputs of the Bx, By and Bz magnetic preamps are given the symbols VBxpa, VBypa and VBzpa respectively. Figure 13.2.1 shows the location of each of these voltages.

The conversion factors and their symbols are listed below. The conversion factors convert the Vdiff values to the voltage at the various sensors.

Symbol	Factor

CFez	1.0	Conversion factor for the Ez antenna

CFbx	24.0	Conversion factor for the Bx Search Coil

CFby	24.0	Conversion factor for the By Search Coil

CFbz	24.0	Conversion factor for the Bz Search Coil

The formulas for converting the Vdiff value to the sensor input voltage are shown below.

VDEx	=	Vdiff	(units are volts rms.)

VEz	=	(CFez)*(Vdiff)

VBxpa	=	(CFbx)*(Vdiff)

VBypa	=	(CFby)*(Vidff)

VBzpa	=	(CFbz)*(Vdiff)

For the electric sensors there may be frequency dependent adjustments necessary because of the interaction of the antenna with the plasma, but these are dependent upon the plasma impedance. If the user wishes to adjust for these effects, see Section 6.0.

8. Now the sensor-dependent calibrations must be applied. For the Bx, By and Bz Search Coils, the voltage at the output of the Search Coil preamplifiers must be converted to nanotesla. See tables 7.1.1 through 7.1.3 in the section about the Magnetic Search Coils for the frequency-dependent conversion factors. For a particular frequency let this conversion factor be given the symbol CBxnt; for example, Table 13.2.1.8.2 shows that at 1000 Hz the Bx Search Coil's response is 147.8 mV/nT, so CBxnt is 0.1478. To convert from voltage at the output of the Bx, By and Bz Search Coil preamplifiers, VBxpa, VBypa and VBzpa must be divided by CBxnt, CBynt or CBznt respectively. This is shown in the following equations:

NTBx	=	VBxpa/CBxnt	(units are nT rms)

NTBy	=	VBypa/CBynt

NTBz	=	VBzpa/CBynt

NTBx, NTBy and NTBz are the fields detected by the Bx, By and Bz Search Coils. At this point we have meaningful physical units. For the electric antennas we have voltage measured at the antenna elements. For the magnetic senors we have the magnetic field in nanotesla at the sensors. Next the magnitude of the electric field for the electric antennas can be obtained. The voltages at the antennas are divided by the effective antenna length, producing units of volts per meter. Here the effective antenna lengths are defined as the physical distances between the geometric centers of the antennas for the Ex dipole and the geometric center for the Ez antenna. The effective length of the Ex+ to Ex- dipole antenna configuration is given the symbol LExdelta. The Ez monopole effective length is given the symbol LEz. For a more detailed discussion of the effective lengths of the electric antennas, see Section 5.

Effective Antenna Lengths in Meters for various mode configurations

Antenna	Effective Length (meters)	Configuration

LExdelta	9.26	dipole

LEz	5.00	monopole

The electric field on the Ex dipole is represented by VMExdelta, and the electric field on the Ez monopole by VMEz. The following equations show the method for calculating the electric field on the antenna in volts per meter. These equations show the method for calculating the electric field on the antenna in volts per meter. These equations do not include effects due to stray capacitive divider effects between the antennas and the spacecraft.

VMExdelta	=	(VDEx)/(LExdetlta)

VMEz	=	(VEz)/(LEz)

9. Finally, to obtain the power spectral density, one must square the value and divide by the bandwidth, which depends upon the type of window function used before performing the FFT. If no window function is used, then the equivalent noise bandwidth is the FFT bin width, which is the sample frequency divided by the number of samples (fs/2N). If the Hanning window

suggested above is used, then the equivalent noise bandwidth is 1.5 times the FFT bin width (again see "Digital Filter Handbook" by Fred Taylor).

13.2.2 Examples of Conversions from Data Numbers to Science Units

As an illustration of how to obtain calibrated values from WFR telemetry, let us look at some real data:

Example 1:	CDS Time	1997-298 T05:17:28.000	(SCLK 4AE3DF87 FC30)

SCET	1997-298 T05:17:27.000	(SCLK 4AE3DF86 FC30)

After the electric antenna deployment, a broad band emission is examined. The WFR mode was cycling between the 40 Hz band and the 2.5 kHz band with 30 dB gain. Lets look at the 2.5kHz Ex dipole data for this example. A waveform of length 512 samples was captured. Following the recipe for obtaining calibrated values, the DC component is computed and subtracted form all the 512 samples. Since the filter mode is 2.5kHz, all 512 samples are then divided by 6136 which has units of counts per volts rms. Then the samples are multiplied by the gain factor, 1060/20 (or 1000). A Hanning window is applied to the data and then all windowed values are multiplied by 2 to offset the Hanning window's coherent gain. A FFT is performed on the data, and after normalizing, the parts of the complex outputs, summing them, and taking the square root. The broad-band emission under examination extends from about 600 Hz to 1700Hz. The peak amplitude occurs at frequency 1060.27 Hz. This peak amplitude is Vdiff at 1060.27Hz.

Vdiff	=	6.58x10-5 Vrms

Since the sensor is the Ex dipole, we know that the voltage VDEx is the same as Vdiff. So the electric field strength can be calculated directly:

VMExdelta	=	(VDEx)/(LExdelta)

=	6.58x10-5 /9.26

=	7.11x10-6	Vrms/meter

Finally, to determine the electric field power spectral density, we must square this value and divide by the equivalent noise bandwidth. Since we have the 2.5 kHz mode, the sample frequecny is given by:

Fs	=	1.0/1.4x10-4

=	7142.9	Hz

and since the sample set size is 512, the FFT bin size is given by

)f	=	Fs / 512

=	7142.9 / 512

=	13.95	Hz

But since a Hanning window was applied to the data, the equivalent noise bandwidth is given by:

ENBW	=	1.5 * )f

=	20.93	Hz

So the power spectral density at 1590.4 Hz is given by

PSD	=	(VMExdelta)2 /ENBW

=	(7.11x10-6)2 / 20.93

=	2.42 x 10-12	Vrms2 / meter2 Hz

Example 2.	Unix Time	1996-214 T01:07:34	(SCLK 32000356 1AB0)

SCET	1996-214 T01:07:24.250 Epoch 0	(SCLK 3200034C 1A60)

During unit level testing the Bx Search Coil was stimulated with a 1 kHz tone at 0.5 Vrms. This should have produced a magnetic field of 0.5nT(rms). The WFR was in the 2.5 kHz mode with 30 dB of gain. A waveform of length 512 was captured. The raw data shows a sine wave with a maximum value of 2555 and a minimum value of 1538, giving an initial estimate of 1017 counts peak-to-peak for the sine wave. Following the recipe for obtaining calibrated values, the DC component is computed and found to be 2051.01 counts. This value is subtracted form all 512 samples. A Hanning window is applied to the data and then all windowed values are multiplied by 2 to offset the Hanning window's coherent gain. A FFT is performed on the data, and after normalizing, the magnitudes of the resulting 256 components are computed by squaring the real and imaginary parts of the complex outputs, summing them, and taking the square root. The peak amplitude occurs at the frequency of 1004.46 Hz, and this peak amplitude is 496.1 counts.

(note that this is close to our initial estimate of 508.5 counts peak for the amplitude). Dividing this by the calibration factor of 6136 counts peak / Vrms and also by the gain factor of 10G/20, we obtain Vdiff at 1 kHz:

Vdiff	=	496.83 /(6136* 1030/20)

=	351.31 / (6136* 31.62)

=	2.56 x 10-3 Vrms

Since the sensor is the Bx Search Coil, we now want to know what the voltage VBxpa from the Search Coil preamplifier is:

VBxpa	=	(CFbx) *(Vdiff)

=	24 * 2.56 x 10-3 Vrms

=	61.44	mVrms

Now referring to the Search Coil calibration in Table 7.1.1, we find that at 1000 Hz the Bx Search Coil's response CBxnt is 147.8 mV / nT. So we find that the magetic field strength NTBx is:

NTBx	=	VBxpa / CBxnt	(units are nT rms)

=	61.44 / 147.8	nT rms

=	0.416	nT rms

This value agrees well with the WBR example 2 in section 12.2. As in section 12.2 it makes little sense to calculate the spectral density since the signal is a tone.

13.3.1 WFR Frequency Response

In this section the frequency response calibration data for the waveform receiver are presented. Transfer functions for each of filters is shown. Figure 13.3.1.1 illustrates the stimulus configuration used for the WFR frequency responses. The oscillator output is attenuated by a fixed amount and a balancing transformer is used to drive the Ex+ and Ex- inputs differentially.

During the calibrations, the HP workstation commands the oscillator to step in frequency. For each frequency step, a waveform is captured and telemetered to the spacecraft simulator. A FFT is performed on the data after removing the DC component. The peak amplitude is chosen from the frequency domain result, and the peak frequency (which should be very close to the stimulus frequency) is chosen. The amplitude is calculated by simple time domain rms average and then is adjusted by square root of two divided by two to give the amplitude of the sine wave in WFR counts. This rms calculation yields a value very close to the FFT result at the peak frequency, but does not suffer from the "scallop loss" effect of the FFT results, which are sensitive to the proximity of the frequency to the center of a FFT bin. For further discussion on this effect, see Section 12.3.2, where the FFT amplitudes of the peak frequencies are presented for the WBR gain calibrations. Finally, the amplitude is expressed in counts peak out per volts rms input.

Although the frequency response could be used to adjust the calibrations of the WFR data, it is recommended that this not be done, since the noise floor becomes accentuated outside the pass-band. Only frequencies inside the pass-band should be adjusted. And data should be ignored if it is outside the 3-dB points. From the frequency response curves, those 3-dB points are approximately:

Filter	Gain	3-dB points

40 Hz	0 dB	2.2 Hz - 26.8 Hz

40 Hz	10 dB	2.5 Hz - 26.8 Hz

40Hz	20 dB	4.5 Hz - 26.8 Hz

40 Hz	30 dB	9.3 Hz - 26.8 Hz

2.5 kHz	0 dB	3 Hz* - 2.56 kHz

2.5 kHz	10 dB	3 Hz* - 2.56 kHz

2.5 kHz	20 dB	5 Hz - 2.56 kHz

2.5 kHz	30 dB	9 Hz - 2.56 kHz

The two 3-dB points in the table above marked with * are extrapolated values calculated from board level test data which show 3-dB break points of 3 Hz for the high pass filter in the 2.5 kHz filter band.

WFR Low Band Frequency Response

Room Temperature

File T960729.U06

Band 40 Hz

Antenna ExLo

WFR Gain 30 dB

Frequency Normalized Output

0.9800000 0.0294155

1.3700000 0.0640782

1.7600000 0.1047824

2.1500001 0.1459476

2.5400000 0.1898210

2.9300001 0.2300148

3.3199999 0.2672539

3.7100000 0.3044979

4.0999999 0.3394885

4.4899998 0.3729623

4.8800001 0.4052884

5.2700000 0.4372225

5.6599998 0.4682141

6.0500002 0.4966799

6.4499998 0.5227515

6.8400002 0.5518564

7.2300000 0.5781877

7.6199999 0.6031932

8.0100002 0.6282924

8.3999996 0.6524822

8.7900000 0.6784075

9.1800003 0.7024354

9.5699997 0.7261289

9.9600000 0.7504578

10.3500004 0.7714002

10.7399998 0.7934631

11.1300001 0.8117408

11.5200005 0.8298280

11.9099998 0.8457571

12.3000002 0.8591852

12.8900003 0.8711307

13.2799997 0.8812733

13.6700001 0.8883258

14.2600002 0.8979663

14.6499996 0.8998978

15.0400000 0.9029118

16.2099991 0.9079832

16.7999992 0.9101573

17.1900005 0.9135265

17.5799999 0.9177758

17.9699993 0.9229839

18.3600006 0.9283523

18.7500000 0.9369215

19.1399994 0.9445062

19.5300007 0.9558038

19.9200001 0.9645656

20.3099995 0.9751027

20.7000008 0.9835373

21.0900002 0.9917958

21.4799995 0.9973176

21.8799992 1.0000000

22.2700005 0.9981878

22.6599998 0.9952689

23.0499992 0.9849772

23.4400005 0.9690644

23.8299999 0.9503459

24.2199993 0.9266265

24.6100006 0.8988805

25.0000000 0.8697878

25.3899994 0.8384596

25.7800007 0.8056284

26.1700001 0.7724604

26.5599995 0.7349731

26.9500008 0.6967620

27.3400002 0.6542301

27.7299995 0.6101620

28.1200008 0.5622446

28.5200005 0.5118249

28.9099998 0.4599399

29.2999992 0.4087435

29.6900005 0.3594084

29.8799992 0.3353098

WFR High Band Frequency Response

Room Temperature

File T960705.U04

Band 2.5 KHz

Antenna ExLo

Gain 30 dB

Frequency Normalized Output

27.900 0.9078102

41.850 0.9715824

83.710 1.0000000

97.660 0.9980220

111.610 0.9945238

125.560 0.9921464

139.510 0.9879963

167.410 0.9900233

195.310 0.9865163

223.210 0.9853725

237.170 0.9822952

251.120 0.9850758

265.070 0.9804959

279.020 0.9824361

306.920 0.9804398

320.870 0.9791099

334.820 0.9801606

362.720 0.9770414

390.620 0.9757941

418.530 0.9741844

432.480 0.9729114

460.380 0.9701056

502.230 0.9672104

530.130 0.9652461

571.990 0.9616783

599.890 0.9594510

641.740 0.9564958

683.590 0.9546308

725.450 0.9508037

781.250 0.9476834

837.050 0.9437379

878.910 0.9404175

934.710 0.9360785

1004.460 0.9317712

1074.220 0.9264954

1157.920 0.9194059

1227.680 0.9133144

1311.380 0.9042442

1381.140 0.8973154

1478.790 0.8873913

1632.250 0.8724679

1715.960 0.8639951

1827.570 0.8525341

1967.080 0.8378108

2078.680 0.8227733

2218.190 0.8015717

2357.700 0.7770430

2525.110 0.7287361

2692.520 0.6192870

2859.930 0.2011404

3055.250 0.0295593

13.3.2 WFR Gain Calibration

In this section, the amplitude calibrations for the waveform receiver are presented. The gain calibrations were done at a limited number of frequencies in the pass band of the filters in the receiver. One stimulus frequency in each of the two bands was chosen for this calibration. The stimulus configuration used for the WFR gain calibration is shown in Figure 13.3.2.1.

The procedure used for the performance of the calibrations is as follows. A command is sent to the oscillator and attenuator to set the desired setting. A waveform is captured by the WFR and telemetered to the spacecraft simulator. An FFT is performed on the WFR capture to determine the frequency. Also the waveform is analyzed in the time domain to determine the rms amplitude in counts rms.

The results are shown in Table 13.3.2.1 for the 40 Hz WFR mode and Table 13.3.2.2 for the 2.5 kHz WFR mode.

Table 13.3.2.1 WFR Low-Band 40 Hz Gain Calibration (@ 24.4 Hz)

WFR	Output	Counts (rms)	Counts / Volt	Counts peak output

Gain	Amplitude	@ Stimulus	normalized	per Volt rms input

Setting	of	amplitude	to	normalized to

(dB)	Stimulus(dB)	& WFR Gain	WFR gain = 0 dB	WFR Gain = 0 dB

0	-60 dB	4.286	4286.77	6062.41

10	- 60 dB	14.012	4430.91	6266.26

20	-60 dB	43.972	4397.16	6218.52

30	-60 dB	128.926	4076.98	5765.72

Table 13.3.2.2 WFR High-Band 2.5 KHz Gain Calibration (@ 1.0 KHz)

WFR	Output	Counts (rms)	Counts / Volt	Counts peak output

Gain	Amplitude	@ Stimulus	normalized	per Volt rms input

Setting	of	amplitude	to	normalized to

(dB)	Stimulus(dB)	& WFR Gain	WFR gain = 0 dB	WFR Gain = 0 dB

0	-20 dB	423.727	4237.27	5992.40

10	-40 dB	135.875	4296.74	6076.51

20	-40 dB	431.357	4313.57	6100.31

30	-30 dB	142.541	4507.53	6374.61

The amplitude calibrations show that the gain amplifiers have small variations in gain from the desired gain change for each filter band. At the frequency that the calibrations were performed, the variations in the gain are less than 1 dB. The gains were calculated by performing a time domain calculation of the amplitude rather than using the amplitude result from the FFT. This eliminates the "scallop loss" mentioned in section 12.3.2. Because of the small variations due to gain settings a single conversion factor can be used for each filter band. These average gain conversion factors are shown in Table 13.3.2.3.

Table 13.3.2.3 WFR Average Gain Conversion Factors

Counts / Volt	Counts peak output

normalized	per Volt rms input

WFR	to	normalized to

Filter	WFR gain = 0 dB	WFR Gain = 0 dB

40 Hz	4298	6078

2.5 kHz	4339	6136

13.3.3 WFR Random Noise Response

Tests were conducted to characterize the response of the Waveform Receiver to random noise. These bench tests were performed on July 28-29, 1996. The 40 Hz band response was performed at +28 degrees C and the 2.5 kHz band response was performed at +40 degrees C. Two test configurations were used. These test configurations are shown in Figures 13.3.3.1 and 13.3.3.2. The stimulus was connected to the instrument Ex+ and Ex- inputs. The noise spectral density was measured using the HP3585A Spectrum Analyzer, and the graphs showing the frequency spectrum for the two stimulus configurations are shown in Figure 13.3.3.3 and 13.3.3.4. Also a measure of the total power was made using a true RMS meter, and an estimate of the noise spectral density was obtained by using that and the signal bandwidth. For each of the WFR modes approximately spectra were averaged. The average spectra for the 40 Hz band are shown in Figures 13.3.3.5 through 13.3.3.8. The average spectra for the 2.5 kHz band are shown in Figures 13.3.3.9 through 13.3.3.12. Using an estimate of the average level for each plot, an estimate of the noise spectral density was done using the calibration procedure described in Section 13.2. Note that the FFT size for all of these tests is 512 samples, and a Hanning window was applied to the data. The results are summarized for the 40 Hz mode in Table 13.3.3.1.

Table 13.3.3.1 WFR 40 Hz Mode: White Noise Response (WFR Gain = 0 dB)

RMS voltage (Vrms)	1.00	1.00	1.00	1.00
Bandwidth (Hz)	200	200	200	200
Attenuation(dB)	30	20	10	0
Est. PSD (dBV/Hz1/2)	-53	-43	-33	-23
HP3585 SD (dBV/Hz1/2)	-54	-44	-34	-24
Avg. WFR PSD (dBV/Hz1/2)	-53	-43	-35	-33

Notice the large discrepancy for the test at 0 dB attenuation. The HP3585 spectrum analyzer measured -24 dBV/Hz1/2, while the WFR measured -33 dBV/Hz1/2. The reason for this discrepancy is that the data was clipped , so a low estimate of the power results. This overloading is apparently just starting to occur at the 10dB attenuation setting, where the WFR estimate is 1 dB lower relative to the tests at the higher attenuations. Those tests at 20 and 30 dB attenuation are both within 1 dB of the HP3585 estimate. The scatter in the data seems to indicate that these are reasonable answers.

Notice that for the 40 Hz test, there was an interference tone present. This 180 Hz tone is a harmonic of the 60 Hz power line and is being input through the stimulus. Nevertheless, it does not interfere with the test. The HP3585 measured the spectral density at 90 Hz, avoiding the noise line, and the WFR PSD estimate is within one dB of that.

The results for the 2.5 kHz filter mode are summarized in Table 13.3.3.2.

Table 13.3.3.2 WFR 2.5 kHz Mode: White Noise Response (WFR Gain - 0 dB)

RMS voltage (Vrms)	1.00	1.00	1.00	1.00
Bandwidth (kHz)	20	20	20	20
Attenuation(dB)	30	20	10	0
Est. PSD (dBV/Hz1/2)	-73	-63	-53	-43
HP3585 SD (dBV/Hz1/2)	-74	-64	-54	-44
Avg. WFR PSD (dBV/Hz1/2)	-74	-64	-55	-51

Figure 13.3.3.3:	HP3585 Spectrum Analyzer Display

WFR 40 Hz Mode White Noise Test

REF 12.0 dBv	MARKER 90.0 Hz

5 dBv/DIV	RANGE 12.0 dBv	-24.5 dBv (1 Hz)

START .0 Hz	STOP 1 000 Hz

RBW 3 Hz	VBW 10 Hz	ST 222 SEC

Figure 13.3.3.4:	HP3585 Spectrum Analyzer Display

WFR 2.5 kHz Mode White Noise Test

REF -18.0 dBv	MARKER 5 000.0 Hz

1 dB/DIV	RANGE 12.0 dBv	-44.2 dBv (1 Hz)

START .0 Hz	STOP 50 000.0 Hz

RBW 30 Hz	VBW 100 Hz	ST 111 SEC

13.3.4 WFR Noise Levels

In this section, the in-flight receiver noise floors are detailed for the commonly used modes. The figure numbers of the in-flight noise floors for these modes are shown in Table 13.3.4.1.

Table 13.3.4.1 List of Figures Showing In-Flight Noise Floors

Figure Sensor	Band	Gain	Comment

13.3.4.1	Ex	2.5kHz	30dB	Antenna Retracted

13.3.4.2	Ex	2.5kHz	30dB	Antenna Extended

13.3.4.3	Ez	2.5kHz	30dB	Antenna Retracted

13.3.4.4	Ez	2.5kHz	30dB	Antenna Extended

13.3.4.5	Bx	2.5kHz	30dB

13.3.4.6	By	2.5kHz	30dB

13.3.4.7	Bz	2.5kHz	30dB

13.3.4.8	Ex	40Hz	30dB	Antenna Extended

13.3.4.9	Ez	40Hz	30dB	Antenna Extended

13.3.4.10	Bx	40Hz	30dB

13.3.4.11	By	40Hz	30dB

13.3.4.12	Bz	40Hz	30dB