Rc

D2 C (A) One-Core Hybrid

RS 50 A T2

V\AA

D2 c (B) Two-Core Hybrid

Fig 6—Hybrid power splitters.

and it must be fed from a source that is matched and resistive at the first few odd harmonics of the oscillator frequency—not just at the fundamental frequency. This is so because the LO port of a diode DBM generates odd harmonics and feeds them back to the source. The LO port of a DBM is also sensitive to odd harmonics in its drive. Any-cross coupling of these odd harmonics between DBMs (through the hybrid) increases the sensitivity of output phase to the drive level.

Because the source must provide a wideband match, you shouldn't use a Wilkinson power divider. Because the oscillator output must be resistive at odd harmonics, you shouldn't drive the hybrid directly from a tuned circuit or low-pass filter. Either use a broadband buffer amplifier to drive the hybrid, or use an attenuator pad and a more powerful LO.

Phase Accuracy Requirements

All of the phase-shift networks discussed so far provide a phase shift that is proportional to frequency. That means you may need to tweak the phase for optimum opposite-sideband rejection if you move very far off the design frequency. So how accurate does the phase have to be? The contribution to opposite-sideband response due to phase errors is one half of the sine of the phase error. A phase error of 1.15° (sine = 0.02) results in an opposite-sideband voltage level of 0.01 times that of the desired sideband, for a rejection of 40 dB. This much phase change would occur if you change the frequency by about 1.3% for any of the previously described phase shifters.

The Quadrature Hybrid

Another network combines the functions of broadband hybrid and phase shifter in a deceptively simple circuit: just one (or two) capacitor(s) and a bifilar inductor. This network, shown in Fig 7A and 7B, is known as an Obstacle Coupler5 or a Twisted-wire Quadrature Hybrid.8 Let's call it a quadrature hybrid. The two versions shown in the figure differ only in whether the capacitor is divided into two parts; opinions differ as to which version is better. Fig 7C shows this hybrid connected in a circuit. When a quadrature hybrid is built with lossless components, the two outputs have a relative phase shift of 90° that is totally independent of frequency. Losses reduce the phase shift slightly; an inductor Q of 50 causes a phase error that yields 46 dB of opposite-sideband rejection.

The quadrature hybrid considered here is just a discrete-component version of the coupled-line quadrature hybrid used at UHF and microwave frequencies. Each of the quadrature outputs looks purely resistive—independent of frequency—as long as both the input port (A) and isolated port (D) have matched resistive terminations. This is another way of saying it really is a wideband hybrid. All four ports have the same impedance level. The output amplitudes of the quadrature hybrid are frequency dependent, with the power split equally only at the design frequency. Fig 8A shows the output amplitude versus frequency for each output, while Fig 8B shows the phase, both with a 50 Q resistive load.

Fig 9A shows the LO drive-current waveforms, and Fig 9B shows the RF port voltages for a quadrature hybrid driving two DBMs. At the design frequency, a circuit using the quadrature hybrid has both relative phase and relative RF output amplitude that are totally insensitive to LO level over the ±10% range.

If you depart from the design frequency the phase stays constant, but the RF amplitude changes because the power-split equality of the quadrature hybrid is frequency dependent. Luckily, the RF output of a DBM (the data sheets call it conversion loss) is relatively insensitive to the LO drive level. As we have already seen in Fig 5 for a resistive source, the sensitivity of RF output amplitude to LO drive level is only of the order of 0.1. This means that a drive change of 10% changes the RF output by only 1%. A frequency change of 10% (from the design frequency of the quadrature hybrid) causes the relative amplitudes of the two LO drive outputs to shift by about 10%, resulting in an RF output shift of about 1%. It takes 2% of RF amplitude shift to degrade the opposite-sideband

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