Measurements of small losses on 1296 using a HP8712C network analyzer.
(Feb 9 2013)

The DUTs


Figure 1. DUTs with SMA connectors.


  • DUT1 About 30 mm of RG 400 cable. Electrical length 0.284 wavelengths.
  • DUT2 Modified connectors. Electrical length 0.243 wavelengths.
  • DUT3 Modified connectors. Electrical length 0.129 wavelengths.
  • DUT4) A pair of adapters. Electrical length 0.252 wavelengths.
  • DUT5) Relay HP8761B with adapters. Electrical length 0.679 wavelengths.
  • DUT6) Relay CX-520-D with adapters. Electrical length 0.0.275 wavelengths.
  • DUT7) Male to male adapter and two female chassis connectors. Electrical length 0.275 wavelengths.
  • DUT8) Modified connectors. Part with high impedance. Electrical length 0.338 wavelengths.

Combinations of the DUTs were also measured. Measurement of DUTs as well as combinations of them gives rise to an overdetermined system of equations from which unknowns can be determined.

DUT18 means DUT1 male connected to DUT8 female and so on.

The Rx port.

The Rx port of the HP8712C network analyzer is nominally 50 ohms. Specifications say that the return loss should be 18 dB. For insertion loss measurements the Rxport (load) should be a male SMA connector while the Tx port has to be a female SMA. Figure 2 shows the measurement of the Rx port impedance. A Flexiform 401 (impedance stable) cable with male N precision connectors in both ends was held in a position as seen in the figure. Open, short and load of the calibration kit were used to calibrate with very small movements of the cable. Finally the Tx port was connected to the Rx port which produced the result in figure 3. Return loss is 20 dB which is well within specification. The SMA to N adapter does not do any harm.


Figure 2. Investigating the Rx port of the HP8712C network analyzer. Here the last step of calibration is done. The calibration kit load is in red colour.



Figure 3. Investigating the Rx port of the HP8712C network analyzer. The magnitude of the impedance error is about 10 ohms. For the measurement of small insertion losses a much better matching is desireable.


There are many ways to make the Rx port well matched. In this study attenuators were used because that particular set of attenuators with a well known impedance will be useful as the Tx port for insertion loss measurements using a radio receiver and a signal generator.

The impedance of the Rx port with and without DUTs.

The setup for impedance as well as insertion loss measurements is shown in figure 4.


Figure 4. The Tx port on the left side is fixed. The Rx port can be moved axially, the black coaxial cable can slide axially in the "third hand."


The Rx port starts with a 3 dB attenuator followed by a 6 dB attenuator and about 1 m of Flexiform 401 cable with an extra screen on it. This cable is in a soft bend and allows the small axial movement with extremely small impedance changes. The cable is followed by a 40 dB attenuator.

The impedance of the Rx port is very insensitive to the impedance of whatever is connected to the other side of the 40 dB attenuator. It does not matter if it is connected to the Network analyzer or to a signal generator.

Raw data for impedances and losses.

Table 1 gives results with links to VNA screen dumps


Device    Zre      Zim      Loss      Equ
         (Ohm)    (Ohm)    (dB)  
none     52.02    0.21    -0.002      1
DUT1     50.34    0.69     0.010      2
DUT3     49.09   -2.56    -0.009      3
DUT4     50.45    0.16     0.024      4
DUT7     51.84   -2.46     0.039      5
DUT13    54.04    2.24     0.071      6
DUT43    52.97    3.10     0.079      7
DUT73    55.71    0.68     0.096      8
DUT37    46.71   -2.12     0.060      9
DUT34    49.16   -0.95     0.058     10
DUT31    49.67   -1.00     0.046     11
DUT8     71.81    0.51     0.198     12
DUT83    75.04    5.42     0.289     13
DUT81    74.35    0.20     0.313     14
DUT813   69.27   -2.47     0.281     15
DUT318   55.75   14.82     0.228     16
DUT381   44.59  -18.52     0.288     17
DUT831   74.80    2.61     0.355     18
DUT183   34.89    3.87     0.199     19
DUT138   59.53   19.49     0.311     20
DUT6     53.04    1.89     0.136      -
DUT18    36.77    4.60     0.214     21
DUT38    45.70  -17.41     0.142     22
DUT48    36.75    0.00     0.207     23
DUT84    73.83    1.24     0.271     24
DUT14    51.73   -0.41     0.108     25
DUT41    51.89   -0.11     0.108     26
DUT5     51.43   -0.19     0.102      -

Table 1. Raw data from the HP8712C network analyzer.

Evaluation of unknowns.

The impedances in table 1 all contain the unknown calibration error from the calibration kit.

The insertion loss should be the sum of the mismatch loss and the sum of the dissipative losses for the DUT. Disregarding DUT5 and DUT6 which are not measured together with other DUTs we have this set of unknowns:

x(1)=The dissipative loss of DUT1
x(2)=The dissipative loss of DUT3
x(3)=The dissipative loss of DUT4
x(4)=The dissipative loss of DUT7
x(5)=The dissipative loss of DUT8
x(6)=The calibration error real part
x(7)=The calibration error imaginary part
x(8)=The Tx port impedance error real part
x(9)=The Tx port impedance error imaginary part
There are 26 equations that connect these 9 unknown variables. For each line in table 1, the loss should be the sum of the dissipative losses plus the insertion loss. The insertion loss can be computed from this formula:

IL = 4 * Rt * Rr / [ (Rt + Rr)2 + (Xt + Xr)2 ]

Rt is the real part of the Tx port impedance.
Xt is the imaginary part of the Tx port impedance.
Rr is the real part of the Rx port impedance.
Xr is the imaginary part of the Rx port impedance.

From the equation it is obvious that we can not determine Xt and Xr separately, only their sum. Also Rt and Rr are strongly coupled. This means that we have 26 equations and 7 independent variables. The RMS deviation produced by a least squares fit will give a good insight in the measurement errors.

A simple Fortran program with a Makefile for Linux can be downloaded here: losscalc100.tbz (5536 bytes) Running it with table 1 as input produces the listing displayed in table 2.

 DUT100  ( 50.340   0.690)   il= 0.0100   Dissipat.= 0.0556  err= 0.0419
 DUT300  ( 49.090  -2.560)   il=-0.0090   Dissipat.= 0.0096  err= 0.0120
 DUT400  ( 50.450   0.160)   il= 0.0240   Dissipat.= 0.0509  err= 0.0227
 DUT700  ( 51.840  -2.460)   il= 0.0390   Dissipat.= 0.0561  err= 0.0163
 DUT130  ( 54.040   2.240)   il= 0.0710   Dissipat.= 0.0653  err= 0.0052
 DUT430  ( 52.970   3.100)   il= 0.0790   Dissipat.= 0.0605  err=-0.0093
 DUT730  ( 55.710   0.680)   il= 0.0960   Dissipat.= 0.0658  err=-0.0144
 DUT370  ( 46.710  -2.120)   il= 0.0600   Dissipat.= 0.0658  err=-0.0019
 DUT340  ( 49.160  -0.950)   il= 0.0580   Dissipat.= 0.0605  err=-0.0046
 DUT310  ( 49.670  -1.000)   il= 0.0460   Dissipat.= 0.0653  err= 0.0129
 DUT800  ( 71.810   0.510)   il= 0.1980   Dissipat.= 0.0771  err= 0.0267
 DUT830  ( 75.040   5.420)   il= 0.2890   Dissipat.= 0.0867  err=-0.0094
 DUT810  ( 74.350   0.200)   il= 0.3130   Dissipat.= 0.1327  err=-0.0055
 DUT813  ( 69.270  -2.470)   il= 0.2810   Dissipat.= 0.1424  err=-0.0175
 DUT318  ( 55.750  14.820)   il= 0.2280   Dissipat.= 0.1424  err= 0.0149
 DUT381  ( 44.590 -18.520)   il= 0.2880   Dissipat.= 0.1424  err=-0.0298
 DUT831  ( 74.800   2.610)   il= 0.3550   Dissipat.= 0.1424  err=-0.0297
 DUT183  ( 34.890   3.870)   il= 0.1990   Dissipat.= 0.1424  err= 0.0283
 DUT138  ( 59.530  19.490)   il= 0.3110   Dissipat.= 0.1424  err= 0.0020
 DUT600  ( 53.040   1.890)   il= 0.1360   Dissipat.= 0.1298  err= 0.0000
 DUT180  ( 36.770   4.600)   il= 0.2140   Dissipat.= 0.1327  err=-0.0175
 DUT380  ( 45.700 -17.410)   il= 0.1420   Dissipat.= 0.0867  err= 0.0413
 DUT480  ( 36.750   0.000)   il= 0.2070   Dissipat.= 0.1280  err=-0.0308
 DUT840  ( 73.830   1.240)   il= 0.2710   Dissipat.= 0.1280  err= 0.0271
 DUT140  ( 51.730  -0.410)   il= 0.1080   Dissipat.= 0.1065  err=-0.0029
 DUT410  ( 51.890  -0.110)   il= 0.1080   Dissipat.= 0.1065  err=-0.0022
 DUT500  ( 51.430  -0.190)   il= 0.1020   Dissipat.= 0.1041  err=-0.0000
 RMS error=  0.02004  alfa= 0.000000  step= 0.000137
 1  DUT1  Dissipative loss=0.0556
 2  DUT3  Dissipative loss=0.0096
 3  DUT4  Dissipative loss=0.0509
 4  DUT7  Dissipative loss=0.0561
 5  DUT8  Dissipative loss=0.0771
 6  DUT6  Dissipative loss=0.1298
 7  DUT5  Dissipative loss=0.1041
 8  Source impedance real part= 57.392
 9  Load impedance real part= 52.835
10  Sum of complex parts=  1.269

Table 2. Results from the evaluation of dissipative losses from insertion losses measured with the HP8712C network analyzer.



The RMS error in the evaluation of the equations is 0.02 dB. That is by far not good enough for a DUT with a resistive loss in the order of 0.05 dB.