Open RF Prototyping

2.1 Coupling and insertion loss

2.2 Isolation and directivity

2.3 Port matching

3.1 Theoretical background

The following is taken from Dunsmore and reproduced here for convenience.

The two key characteristics of directional couplers, as the name implies, are the ability to sample (or couple) signal flow, and to do so in only one direction. A resistive bridge, if driven in the proper way, also has this directional property. Figure 5 shows a bridge structure. A sample of the drive voltage is present across each resistor. If the bridge is balanced, \(R_1 \times R_3 = R_4 \times R_5\), then no voltage appears across \(R_2\). For balance, the bridge often has all the resistors the same value, say 50 ohms, but the balance only requires that the ratios of each string be equal (\(R_1/R_5 = R_4/R_3\)).

Figure 6a shows a bridge with non-symmetric resistors, driven in the forward signal flow direction. In this case the voltages across certain nodes have been labeled consistent with the coupler in Figure 4. For the resistors chosen, \(V_{coup}\) is 16 dB down from \(V_{p2}\) (16 dB coupling), and \(V_{p1}\) is 1.5 dB down from \(V_{p2}\) (1.5 dB loss). The equations shown in Figure 6a demonstrate how to calculate resistance values for any coupling factor.

The directional nature of the bridge is demonstrated by redrawing the figure to put a voltage source in series with the \(V_{p1}\) resistor, and "stretching" the remaining elements about to achieve Figure 6b. Note that none of the connections have been changed, except moving the drive voltage from port 2 (\(V_{p2}\) resistor) to port 1 (\(V_{p1}\) resistor). Drawn this way, it is easy to see that no voltage appears across the coupler port (\(V_{coup}\) = 0), as the bridge is balanced in this fashion.

In the RF implementation of this bridge, the \(V_{p2}\) resistor represents the port 2 impedance (50 ohms in this case), the \(V_{coup}\) resistor represents the coupled port impedance, and \(V_{p1}\) resistor represents the port 1 impedance. The difficulty with this structure is that port 1 must be isolated from ground; this may be accomplished with a transformer of some sort. Figure 7 shows a diagram of the bridge, with the port 2 and coupled port represented by coaxial transmission lines, and port 1 isolated by a transformer. The 1:1 transformer may be realized in a clever way by using a ferrite loaded coaxial transmission line balun.

The implementation of the 1:1 transformer might use a simple wire-wound core, but the low frequency response is limited by the mutual inductance, and it is difficult to maintain a constant impedance at high frequency. The 1:1 transformer function can be approximated by using a length of coaxial cable, with a ferrite bead on the outer conductor. This forms a balun, which has a constant 50 ohms impedance from the inner to outer conductor. One or more ferrite beads raises the impedance of the outer conductor to ground by the impedance of the bead. In the brideg structure, this is a parasitic impedance which may be modeled as a resistor in parallel with an inductor, from the outer conductor to ground. Varying the inductive index allows using a high frequency, low permeability (\(\mu\)) bead near the bridge structure, with a low frequency, high \(\mu\) bead following to raise the low frequency inductance.

3.2 Board performance comparison

Selection of RF connectors is critical to the performance of the board.

3.3 Polynomial fits for insertion loss and coupling

Polynomial fits to the coupler S21 (insertion loss) and S23 (coupling) are carried out on the average of the responses measured for the prototype boards listed in Table 2.

For the insertion loss, a linear fit gives good results as shown in Figure 7. For the coupling a 7th order polynomial is used with the result shown in Figure 8. The equations of the fits are:

For insertion loss:

with:

For coupling:

with: