Quadrature-phase-shift-keying (QPSK) modulation is an effective means of achieving high bandwidth efficiency in wired or wireless communications systems. QPSK modulation can be generated with a direct-digital-synthesizer (DDS) approach, which requires additional components, and tends to be expensive and consume power. An alternative method employs two mixers, one set to a fixed RF and the other driven by a voltage-controlled oscillator (VCO). However, mixing frequencies must be carefully chosen to avoid intermodulation, and the cost of the two local oscillators (LOs), two phase-locked loops (PLLs), two mixers, and several filters can be expensive. A better, cost-effective technique for generating QPSK follows.

Employing just a few components, it is possible to cover more than an octave (2:1 frequency ratio) tuning range with a simple VCO using a fixed inductor and varactor diode (with variable capacitance). This VCO can then be used with any one of several commercial quadrature modulators for direct modulation of baseband in-phase (I) and quadrature (Q) signals into QPSK modulated RF signals.

One problem with using mixers to generate direct modulation is the amount of unwanted harmonic signals, which can cause interference in RF channels outside the band of interest. For a fixed RF, the harmonic problem can often be avoided by using a filter with a fixed RF passband. But if the RF output frequency must be variedas is this example filtering the harmonics is much more difficult and much less effective.

Even-order harmonics, including second harmonics, are typically 35 to 40 dB down from a desired carrier. Often, it is odd harmonics that are more of a concern. All mixers, no matter what kind, generate high-level odd harmonics, especially third harmonics. In the mixing process, the nonlinear mixing elements, such as diodes, act as switches, making rapid transitions from on to off. These rapid transitions generate higher-order harmonics, especially odd-order (third, fifth, etc.) harmonics. In fact, the level of the third harmonic is typically one-third the amplitude of the desired output signal, or only about -10 dBc. The amplitude of the fifth harmonic is about 20 percent that of the desired output signal or about -14 dBc.

Because of the high levels of these harmonics, double conversion is commonly used in communications receivers. Mixing frequencies in a double-conversion scheme are carefully chosen so that harmonic signals and intermodulation products fall in spectral locations where they can be effectively filtered out. Although a DDS generates a QPSK RF signal using sample pulses with high harmonic content, the sample rate is so high that the alias frequency components can easily be filtered out.

Although many modulators or multipliers claim linear performance, mixing and multiplication are a result of nonlinearities. The distinction between mixers and multipliers is that mixers employ elements as switches deliberately commutated between on and off states. This fast switching generates a large number of mixer products at harmonics of the LO frequency, requiring filtering. Still, mixers are popular because they are relatively simple and generate an output that is nearly insensitive to the amplitude of the LO.

Multipliers also work because of the nonlinear circuit elements, although these elements operate smoothly and without the sharp discontinuities of switches. Multipliers are more complex than switches and are sensitive to changes in LO amplitude. If the LO amplitude changes by 20 percent, the output of the multiplier also changes by 20 percent. The output is linearly sensitive to the amplitude of both the LO and the baseband signal. For want of a better term, a multiplier can be thought of as a linear-modulator.

When a linear multiplier is used with a pure sinewave modulation signal, the baseband I and Q signals are directly modulated to RF and theoretically there are no second-, third-or higher-order harmonics. When an LO source of pure sinewave energy is available, several commercial linear multipliers (usually based on Gilbert cells) can be used as modulators. Unfortunately, to generate quadrature modulation, two LO sinewave generators are needed, with equal amplitude but offset in phase by 90 deg. This requirement applies over the full desired range of the RF output. It is not difficult with the proper sinewave source to generate two sinewave signals which are precisely 90 deg. apart and of equal amplitude, at one frequency (refer to the product notes for the model AD835 mixer from Analog Devices, www.analog.com). But achieving the same thing over even a limited frequency range is difficult.

(Fig. 1) shows a simple RC circuit. If a sinewave voltage is applied, the voltage across the resistor *always *leads the voltage across the capacitor by exactly 90 deg., *independent of the frequency*. This is because the current, which flows through the resistor, also flows through the capacitor and since the voltage across a capacitor lags the current by 90 deg., there is always a 90-deg. difference between the voltage across the capacitor and the voltage across the resistor. This exact 90-deg. phase shift is independent of the value of either the resistor or the capacitor.

At just one frequency (1/RC), the two modulating voltages are equal. However, if the band covers a full octave, the voltage amplitudes vary by 3 dB. When these two modulating signals feed two multipliers, the resulting I and Q channels are always well isolated because of the exact 90-deg. phase shift, but the modulated amplitudes of the I and Q channels will also vary by 3 dB, an unacceptable amount.

The modulating voltages must be nearly equal over the band of interestfor example, an octave. To accomplish this, it is necessary that the capacitance impedance be nearly constant or, C = k/f where k is a constant and f is the mixing frequency.

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A traditional VCO is built with a varactor diode and is tuned by varying the reverse voltage across it. The LC tank circuit (Fig. 2)** ** typically has a fixed inductor, but its resonant frequency can be changed by varying the DC voltage across the varactor. To achieve a one-octave frequency range, the varactor's capacitance must change by a ratio of 4:1. Many commercial varactor diodes are available with a capacitance range of 4:1; in fact, a capacitance range of 6:1 is not unusual. Using a varactor with 6:1 capacitance range can yield a frequency range of almost 2.5:1.

If another identical varactor has the same voltage across it as in the VCO, its capacitance is essentially the same as the varactor in the tank circuit. More important, as the DC tuning voltage is changed, the capacitances closely track each other. This tracking feature is key to getting a suitable frequency-dependent capacitance in the in the multiplying modulator.

Another varactor cannot directly be used in the RC circuit to generate the two modulating signals because its capacitance changes by C = k/f^{2}. Whereas a fixed capacitor yields large amplitude variations over a frequency range, a capacitor with this strong frequency dependence also provides large amplitude variations. The varactor's capacitance is changing too rapidly with frequency.

A way to mitigate this too-rapid change is to put another fixed capacitor in series or parallel with the varactor. For example (if things are normalized), let the varactor capacitance vary 2 > C > 0.5 as the frequency varies from 0.7 (Fig. 3).** ** If a fixed capacitor of value 1 is placed in parallel with this varactor, then this combination has nearly constant reactance over this frequency range. In fact, the total capacitive impedance change over this frequency range is only 1.061, corresponding to 0.26 dB. Compare this to 3 dB for the fixed capacitance. To get a capacitive reactance four times higher, simply place a fixed capacitor of value 1 in *series *with the varactor.

Although it's not likely needed (because of other component tolerances), even better amplitude accuracy can be obtained by using a combination of series-parallel capacitors. For example, a better than 1-percent amplitude accuracy can be maintained over the 0.7 to 1.4 normalized frequency range by paralleling the varactor with a 0.25 normalized fixed capacitor and putting a 2.2 fixed capacitor in series with the paralleled combination. There are other combinations that also give an accurate constant-amplitude response across a frequency range wider than 2:1.

As an example of a low-cost QPSK modulation solution, consider the simple VCO tuned by a varying voltage across its varactor (Fig. 4).** ** Feed its sine RF output into a basic RC network composed of a fixed capacitor and another identical varactor. The two equal-amplitude sinewave outputs are 90 deg. apart. These are fed into a commercial multiplier to generate a QPSK RF signal with low harmonics. This arrangement uses few parts, is low in cost, low in power, and delivers direct QPSK modulation over an octave RF frequency range. And it requires no filters. The key to this scheme is that the LO and the I and Q multiplying modulator use identical varactors which operate off the same DC tuning voltage. Once the LO frequency is set, the variable capacitance in the modulator RC circuit is automatically set to the correct value. No other circuit controls are necessary to assure proper tracking (note that components marked with an asterisk are high-value and behave as short circuits or open circuits).