(Feb 22 2013)


Four cables and combinations of them is the set of DUTs for which this page is an attempt to evaluate mismatch losses using a HP 8712 C network analyzer. Insertion losses are better studied in a different circuit where impedances can be better controlled.

DUT1 = 0.125 wl 75 ohm, "TV cable"
DUT2 = 0.125 wl 50 ohm, RG223
DUT3 = 0.25 wl 50 ohm, RG223
DUT4 = 0.25 wl 50 ohm, RG223

See figure 1.

Figure 1. The four cables. Three of them RG223, one a 75 ohm TV cable with foam dielectric and a foil screen surrounded by a very thin braided screen. Two layers of braided screen are applied outside the original screen to make the cable RF tight.

The signal source, a reference impedance.

For measurements of NF and insertion loss a precision signal source is required. The source port is a male BNC connector which is one side of a N to BNC adapter. The N connector goes to two series connected 3 dB attenuators model NAT-3 from Minicircuits. Behind the attenuators is about 1 m of Flexiform 401, an impedance stable cable. The cable is equipped with two precision male N connectors and two extra braided screens since the cable alone is not well enough screened to avoid pick up of interference from the computers. The signal is generated in a HP 8657 A which is connected to a well screened 40 dB power attenuator. From the attenuator to the Flexiform cable about 1 meter of 3.5 mm semirigid coaxial cable is connected via precision N connectors.

The signal source is adjusted to make the impedance the same regardless of whether DUT2 is inserted or not. First by selecting the most suitable attenuator (I have several of them.) As a second step the semirigid cable is squeezed on suitable points until the impedance is the same with and without DUT2.

The procedure should ensure that the signal source has the same impedance as the characteristic impedance of DUT2. The network analyzer finds that to be 49.4 ohms. See figure 2.

Figure 2. The Tx port.

The true impedance is of course unknown. I do not know the accuracy of the instrument or the calibration kit (home-made) that was used for calibration. The impedance error is most probably smaller than 1 ohm however.

When DUT2 is inserted the impedance is nearly unchanged. See figure 3.

Figure 3. The impedance of DUT2 when connected to the tx port.

The receive port for insertion loss measurements.

Fot the insertion loss measurements it is desireable to have an rx port that is a BNC female that has the complex conjugate impedance to match the impedance shown in figure 2.

For the receive port three 3 dB attenuators are series connected followed by a circulator and one more 3 dB attenuator. A male BNC to female N adapter is used to make the rx port match the tx port connector-wise. The circulator ensures that the low noise amplifier that follow will always see the same impedance. The attenuator on the output of the circulator ensures a reasonable input impedance for the amplifier on all frequencies. The three 3 dB attenuator on the input side of the circulator ensure an impedance that does not vary much with the frequency. These attenuators are selected to present an impedance near the complex conjugate impedance in figure 2. See figure 3.

Figure 3. The rx port. This Smith diagram is corrected for the length of the male to male BNC adapter needed to connect the network analyzer to the Rx port. It is assumed that the adapter is matched to 50 ohms.

Impedance transformation in DUTs.

The tx port impedance is selected for DUT2 to cause a very small impedance transformation. One might expect that the similar cable DUT4 would also give a very small transformation, but that is not quite true. The reason could be the cable or differences in how the connectors are mounted. Table 1 gives the measured impedance on 144 MHz at the female end of the different DUTs when the male end is connected to the Tx port.

The mismatch loss is computed from this formula:

Loss = -10 * log10[ 4 * Rs * Rl / { (Rs + Rl)2 + (Xs + Xl)2 } ]

Rs and Xs is the real and imaginary part of the source impedance. Rl and Xl is the real and imaginary part of the load impedance.

device         Zre  Zim       Loss
                (ohms)       (dB)  
Rx port      49.48  -0.26
Tx port      49.41  -0.05   0.00005   
DUT1         56.11  19.97   0.16591
DUT2         49.47  -0.06   0.00005
DUT3         50.59   0.90   0.00071
DUT4         50.13  -0.02   0.00022
DUT13        57.82  19.71   0.16672
DUT31        70.06 -12.06   0.17655
DUT123       54.44  20.10   0.16538
DUT132       57.64  19.68   0.16572
DUT312       70.02 -12.29   0.17788
DUT213       38.09 -12.63   0.16719
DUT231       34.03   5.81   0.17039       
DUT42        50.15   0.01   0.00022
DUT24        48.70  -0.11   0.00034
DUT34        50.65   0.18   0.00060
DUT32        50.55   0.84   0.00064
DUT23        48.29  -0.92   0.00128
DUT43        49.05  -1.22   0.00106

Table 1 Impedance and mismatch loss for the different DUTs. Here it is assumed that the male to male BNC adapter does not cause any impedance transformation.