Transit Time, Dispersion Effect

Author: Leonard Krugman

In the earlier chapters it was noted that the low-frequency, small-signal parameters change as the operating frequency is increased appreciably above the audio range. Figure 7-1 illustrates the low-frequency equivalent circuit of the transistor including the collector junction capacitance C_c. At higher frequencies this equivalent circuit must be modified to include the effects of the current carriers' transit time on the transistor parameters. The transit time of the carriers (holes or electrons) is one of the major factors limiting the high frequency response of the transistor.

Fig. 7-1. Low-frequency equivalent circuit of the transistor (including collector junction capacitance).

The movement of holes or electrons from the emitter through the base layer to the collector requires a short but finite time. In the transistor, as noted earlier, the electron does not have a clear and unimpeded path from emitter to collector. As a result, the transit time is not the same for all electrons injected into the emitter at any one instant. The effect of an identical transit time for all electrons would be a simple delay in the output compared to the input signal. Because the injected carriers do not all take the same path through the transistor body, those produced by a finite signal pulse at the emitter do not all arrive at the collector at the same time. The resulting difference is very small and is of no consequence in the audio frequency range. At the higher frequencies, however, this difference becomes a measurable part of the operating cycle, and causes a smearing or partial cancellation between the carriers. Figure 7-2 illustrates the dispersion effect in a transistor at high frequencies. Notice that, in addition to the increased period, the signal has also suffered a reduction in amplitude (the time delay results in a phase shift). The decrease in the output signal means a decrease in the current gain . The degradation in frequency response becomes steadily worse as the operating frequency is increased, until eventually there is no relationship between the input and output waveforms (and no gain).

Fig. 7-2. Transistor high-frequency dispersion effect.

Another factor that limits the high frequency response of the transistor is the capacitive reactance of the emitter input circuit, which behaves as if r_e is shunted by a capacitor. This reactive parameter is reduced if the source impedance is made as low as possible. Since r_b is also effectively in series with the source, a good high frequency transistor must have a low base resistance. If the source impedance and base resistance are low, the upper frequency response limit is determined primarily by the collector junction capacitance and the variation in the current gain.