Testing of Sigma-Delta Power Amplifier

GISMO Calibration Results

December, 2007

Center for Remote Sensing of Ice Sheets

University of Kansas

Table of Contents

1. Overview

1

2. Calibration

Delay Line Measurements

1

Network Analyzer Measurements

2

1. Overview

The purpose of this document is to discuss the results from the calibration measurements performed to complement the September 2007 airborne field experiment in Greenland.

2. Calibration

2.1 Delay line measurements

For this part of the calibration the radar was configured in a loop-back mode where the transmit waveform is branched into six different paths after passing through a set of high power attenuators and an optical delay line. This is to feed each of the six receiver channels while simulating propagation of the transmit signal through ice. The experimental setup for this part of the calibration is illustrated in Figure 1. Several files were collected using this configuration with the radar operating at 150 MHz and 450 MHz, respectively. A list of the recorded data can be found in the field notes.

Figure 1: Delay line calibration setup. A high power blanking switch and band-pass filter are included as part of each receiver.

2.2 Network analyzer measurements

2.2.1 Calibration of the simulated target

The complex transmission coefficient for the delay line setup was measured using an 8722D network analyzer. This measurement is used to correlate the time delay measured with the network analyzer to that obtained using the radar operating in loop-back mode. Further, the phase and amplitude unbalance between the signals injected to each receiver can be obtained in this step. For convenience, the delay path was divided into four parts:

1) 1:8 power splitter including output cables and 40+10 dB attenuators at the input (red).

2) Optical delay line with input and output cables (green)

3) 2-way power combiner (grey)

4) High power attenuator networks (AN0 and AN1) with cables (light grey)

Each part above was measured individually and the corresponding scattering parameters were recorded using a laptop computer. For the 1:8 power splitter, the transmission coefficient was measured for each of the six used ports with the unused outputs terminated with 50-ohm matched loads (Figure 2). Figure 3 shows the experimental results for the power splitter portion of the setup while the measured response for the fiber optic delay line appears in Figure 4. Table 1 presents all the different delay contributions of the delay chain from the high power attenuator networks to each receiver input. It can be seen from this table that the amplitudes are balanced within 0.8 dB and the delays within less than 0.1 ns.

Figure 2: Measurement setup to determine the phase and amplitude unbalance of the 1:8 power splitter. The network analyzer was also used to obtain the transmission coefficients of the rest of the components in the delay line network.

-120

-100

-80

-60

-40

-20

0

0.E+00

2.E-08

4.E-08

6.E-08

8.E-08

1.E-07

Time delay [s]

Magnitude [dB]

Channel 1 (3.536 ns, -60.9 dB)

Channel 2 (3.538 ns, -61.1 dB)

Channel 3 (3.54 ns, -61.0 dB)

Channel 4 (3.566 ns, -60.6 dB)

Channel 5 (3.54 ns, -61.4 dB)

Channel 6 (3.53 ns, -61.3 dB)

Figure 3: Measured time-domain response for each of the ports of the 8-way power divider with 6 cables connected, unused ports terminated and 40+10 dB attenuators at the input port. During the delay line calibration on 09/24/2007, a slightly longer cable (4.28 ns vs. 3.53 ns) was used on port 2.

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

Time delay [s]

Magnitude [dB]

Delay line (19.99 us, -13.32 dB )

Figure 4: Measured time-domain response for the optical delay line including input and output cables.

AN1

2-way divider

Delay line

1:8 Splitter

Total

Delay

7.79 ns

2.3 ns

19.99 us

Ch1

3.536 ns

20.003626 us

Attenuation

-64.1 dB

3.25 dB

-13.32 dB

-60.9 dB

-135.07 dB

Delay

7.79 ns

2.3 ns

19.99 us

Ch2

3.538 ns

20.003628 us

Attenuation

-64.1 dB

3.25 dB

-13.32 dB

-61.1 dB

-135.27 dB

Delay

7.79 ns

2.3 ns

19.99 us

Ch3

3.54 ns

20.003630 us

Attenuation

-64.1 dB

3.25 dB

-13.32 dB

-61 dB

-135.17 dB

Delay

7.79 ns

2.3 ns

19.99 us

Ch4

3.566 ns

20.003656 us

Attenuation

-64.1 dB

3.25 dB

-13.32 dB

-60.6 dB

-134.77 dB

Delay

7.79 ns

2.3 ns

19.99 us

Ch5

3.54 ns

20.003630 us

Attenuation

-64.1 dB

3.25 dB

-13.32 dB

-61.4 dB

-135.57 dB

Delay

7.79 ns

2.3 ns

19.99 us

Ch6

3.53 ns

20.003620 us

Attenuation

-64.1 dB

3.25 dB

-13.32 dB

-61.3 dB

-135.47 dB

AN0

2-way divider

Delay line

1:8 Splitter

Total

Delay

7.68 ns

2.3 ns

19.99 us

Ch1

3.536 ns

20.003516 us

Attenuation

-63.4 dB

3.25 dB

-13.32 dB

-60.9 dB

-134.37 dB

Delay

7.68 ns

2.3 ns

19.99 us

Ch2

3.538 ns

20.003518 us

Attenuation

-63.4 dB

3.25 dB

-13.32 dB

-61.1 dB

-134.57 dB

Delay

7.68 ns

2.3 ns

19.99 us

Ch3

3.54 ns

20.003520 us

Attenuation

-63.4 dB

3.25 dB

-13.32 dB

-61 dB

-134.47 dB

Delay

7.68 ns

2.3 ns

19.99 us

Ch4

3.566 ns

20.003546 us

Attenuation

-63.4 dB

3.25 dB

-13.32 dB

-60.6 dB

-134.07 dB

Delay

7.68 ns

2.3 ns

19.99 us

Ch5

3.54 ns

20.003520 us

Attenuation

-63.4 dB

3.25 dB

-13.32 dB

-61.4 dB

-134.87 dB

Delay

7.68 ns

2.3 ns

19.99 us

Ch6

3.53 ns

20.003510 us

Attenuation

-63.4 dB

3.25 dB

-13.32 dB

-61.3 dB

-134.77 dB

Table 1: Loss and phase delay budget for from the input of AN0 and AN1 to the input of each receiver.

2.2.2 Measurement of relative phase and amplitude unbalance.

An additional set of measurements was performed in the laboratory in order to validate the results as obtained from the loop-back characterization. The total receiver gain and phase response for each receiver channel was measured with the network analyzer for both 150 MHz and 450 MHz. A 40 dB attenuator was placed at the input of the receiver under test to avoid saturating the amplifiers. Figures 5 and 6 show the measured response for both bands of operation. The effect of the 40 dB attenuator was subtracted from the measurement by removing its loss from the gain plots and its time delay from the time domain responses.

0.12

0.125

0.13

0.135

0.14

0.145

0.15

0.155

0.16

0.165

0.17

0.175

0.18

Frequency (GHz)

0

20

40

60

80

Rx0 (71.33 dB)

Rx1 (71.49 dB)

Rx2 (71.93 dB)

Rx3 (71.23 dB)

Rx4 (71.67 dB)

Rx5 (71.47 dB)

(a)

-60

-50

-40

-30

-20

-10

0

10

20

30

40

0.E+00

1.E-07

2.E-07

3.E-07

4.E-07

5.E-07

6.E-07

7.E-07

8.E-07

9.E-07

Time delay [s]

Relative magnitude [dB]

Rx0 (98.1 ns)

Rx1 (97.0 ns)

Rx2 (97.3 ns)

Rx3 (96.56 ns)

Rx4 (95.15 ns)

Rx5 (97.9 ns)

(b)

Figure 5: Measured response for the 150 MHz receivers: (a) gain and (b) phase unbalance.

0.4

0.425

0.45

0.475

0.5

Frequency (GHz)

0

10

20

30

40

50

60

70

Rx0 (67.9 dB)

Rx1 (67.83 dB)

Rx2 (68.88 dB)

Rx3 (67.60 dB)

Rx4 (68.28 dB)

Rx5 (66.8 dB)

(a)

-60

-50

-40

-30

-20

-10

0

10

20

30

0.E+00

1.E-07

2.E-07

3.E-07

4.E-07

5.E-07

6.E-07

7.E-07

8.E-07

9.E-07

Time delay [s]

Relative magnitude [dB]

Rx0 (75.6 ns)

Rx1 (75.5 ns)

Rx2 (72.7 ns)

Rx3 (76.9 ns)

Rx4 (79.4 ns)

Rx5 (80.0 ns)

(b)

Figure 6: Measured response for the 450 MHz receivers: (a) gain and (b) phase unbalance.

From these measurements the relative phase and amplitude mismatch between channels can be obtained taking one receiver as a reference. Comparing all receivers against channel 1 (Rx0) the following figures are obtained (Tables 2 and 3). These results agree reasonably well with those obtained from the loop-back mode test data. The amplitude errors between the two methods are within 1 dB for both frequencies. For 150 MHz the phase discrepancies range between 7.8-16.68 degrees while being 0.4-34 degrees for 450 MHz.

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6

Amplitude [dB]

0

-0.95

0.50

0.19

-0.15

-0.25

Phase [deg]

0

-64.6

-42.9

-84.7

-162.8

-11.12

Table 2: Relative phase and amplitudes for 150 MHz center frequency obtained from network analyzer measurements.

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6

Amplitude [dB]

0

-0.27

0.88

0

-0.12

-1.45

Phase [deg]

0

-10.7

-156.3

71.8

201.6

237.2

Table 3: Relative phase and amplitudes for 450 MHz center frequency obtained from network analyzer measurements.

The total delays from the output of the power amplifiers to the input of each A/D channel according to the network analyzer data are summarized in Table 4. A delay of 3.7-3.8 ns is included in the calculation to account for the 10-inch cables that connect the receivers to the A/Ds. These results match the figures obtained from the loop-back mode test data within 50 ns.

150 MHz

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6

Delay [us]

20.1031

20.1019

20.1023

20.1015

20.100

20.1029

450 MHz

Ch1

Ch2

Ch3

Ch4

Ch5

Ch6

Delay [us]

20.0807

20.0805

20.0778

20.082

20.0844

20.0851

Table 4: Total time delay based on network analyzer measurements.

2.2.3 Antenna measurements.

The purpose of the antenna network analyzer measurements is to determine the relative phase difference between elements which is caused by differences in length of the feed cables. The experimental setup is illustrated in Figure 1. The unused antenna elements were terminated with 50-ohm loads. The antenna delays as obtained using the network analyzer are summarized in Table 5.

Figure 7: Experimental set up for characterizing antennas.

Element

Delay [ns]

Left 1

69.36

Left 2

64.29

Left 3

64.13

Left 4

64.01

Element

Delay [ns]

Right 1

65.22

Right 2

65.08

Right 3

63.70

Right 4

64.94

Table 5: Relative time delays obtained for the antennas using the network analyzer.

During operation in depth sounder mode, a weighted feed network was used for the transmit array (left wing). The feed network incorporated adjustable line stretchers, which were adjusted in the field to match the transmit antenna elements to less than 0.2 ns and 0.1 dB. No phase matching was implemented on the receive array in depth sounder mode or ping-pong mode.

Power Amplifier

Gain [dB]

Gain [dB]

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