DISCRETE-SIGNAL ANALYSIS AND DESIGN- P11:Electronic circuit analysis and design projects often involve time-domain and frequency-domain characteristics that are difÞcult to work with using the traditional and laborious mathematical pencil-and-paper methods of former eras. This is especially true of certain nonlinear circuits and sys- tems that engineering students and experimenters may not yet be com- fortable with. | 36 DISCRETE-SIGNAL ANALYSIS AND DESIGN to return to the time domain with the confidence that these two equations especially in discrete sequences do not require linearity or superposition. We will use this idea frequently in this book. A two-tone input signal of adjustable peak amplitude will be processed by a circuit that has a certain transfer characteristic which is similar to the Child-Langmuir equation Seely 1956 pp. 24 and 28 Eq. 2-14 as derived in the early 1920s from Poisson s equation for the electric field in space-charge-limited diodes and also many common triode vacuum tubes Iout n KVg n 1 5 2-3 The input base-to-emitter or grid-to-cathode two-tone signal at frequencies f i and f 2 is Vg n Vs nn cos 2n 11 cos 2n J2 Vdc 2-4 V s is the peak amplitude 1 2 of pk-to-pk of each of the two input signals. Vdc is a bias voltage that determines the dc operating point for the particular device. This and a reasonable V s value are found from Handbook V-I curves the maximum peak-to-peak signal is four times Vs . The peak-to-peak ac signal should not drive the device into cutoff or saturation or into an excessively nonlinear region. Figure 2-5 is a typical approximate spectrum for the two-tone output signal. The input frequencies are f i and f 2 and the various intermodulation products are labeled. Adjusting V s and V dc for a constant value of peak desired per-tone output shows how distortion products vary. Note also the addition of 70 dB to the vertical axis. This brings up the levels of weak products so that they show prominently above the zero dB baseline we are usually interested in the dB differences in the spectrum lines . Note also that the vertical scale for the spectrum values is the magnitude in dB because the actual values are in many cases complex and we want the magnitude and not just the real part we neglect for now the phase angles . Note that in this example we let Mathcad calculate Vsig n 1-5 directly the easy way not by using discrete math the hard
