The Digital Quadrature Modulator

The foregoing sections provided a foundation for understanding modulation, number representation in the digital domain, and a method for generating a sampled sinusoid. These three concepts are required for a firm understanding of digital modulation. The fundamental building blocks of a digital quadrature modulator are essentially the same as those for the analog single-sideband modulator shown in figure 1b.

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The digital version is shown in figure 4 — the main difference being that the two multipliers, the adder, and the carrier signals are all made of digital building blocks.

The model shown in figure 4 can be readily implemented using digital hardware. The digital makeup of the NCOs was discussed earlier. Multipliers and adders, too, are readily designed from elemental digital building blocks (AND, OR and NOT units). The only real constraints are the maximum possible sampling frequency (which is mostly dependent on the semiconductor process) and power dissipation.

There is one fundamental rule that cannot be overlooked in digital modulation. Both the digital carrier signal and the digital message signal must be sampled at the same rate. In some instances, the message signal consists of a digital signal sampled at a rate less than the carrier. Such situations require that the message signal be digitally up-sampled to match the carrier sample rate. However, this is another topic altogether and is well beyond the scope of this article. Sample rate conversion techniques are rigorously covered in the existing literature.

Returning to figure 4, the digital quadrature modulator has two message signal inputs: X and Y. In addition, two NCOs produce the quadrature carrier signals. The same system clock and frequency control number are provided to both NCOs. However, one NCO has a cosine wave stored in its ROM while the other NCO has a sine wave stored in its ROM. The carrier frequency (fc) is determined by the frequency control number.

Typically, the X and Y input signals are intended to be quadrature components. For example, if X were a digital cosine wave of frequency fm, and Y were a digital sine wave of the same frequency, then the output of the quadrature modulator would be a single-sideband tone of frequency fc - fm. The Appendix contains a Mathcad program that precisely models this scenario. For other scenarios, simple modifications can be made to the program. For example, an upper sideband can be generated by simply changing the sign of the operator from + to - in the right-hand portion of the “QuadModi” statement.

If a double-sideband signal is desired simply replace Yin(i) in the right-hand portion of the “QuadModi” statement with Xin(i). The NCO ROM parameters, N and D, can also be changed to see the effects of both frequency and amplitude resolution. The system sample rate (Fs) and carrier frequency (Fcarrier) can both be changed, as well. Note, however, that the actual carrier frequency (Fc) may not exactly match the value entered for Fcarrier. This is due to the fact that the frequency control number (FCN) for the NCO must be an integer value because it controls the modulus for a binary counter. This restriction means that only finite frequency resolution is possible. Specifically, only those frequencies that correspond to the FCN values are possible.

This article has demonstrated the key elements of digital quadrature modulation. The high speeds available from today's semiconductor processes make it ever more practical to implement modulation functions in digital rather than analog technologies.

This trend will likely continue as digital semiconductor technology pushes operating speeds ever higher. It should be kept in mind that the end result of implementing analog functions in the digital domain is a time sequence of digital numbers, a natural consequence of the sampling process. However, this number stream must ultimately be converted to an analog waveform to be of any practical use. Thus, a digital-to-analog converter (DAC) must be employed to transform the digital signal into the analog domain. As such, there is still a significant role for analog circuitry, especially DACs. As both sample rate and resolution increas