3-49 Linearity of the trapezoidal waveform, produced by the circuit in figure 3-50, view (A) and view (B) depends on two factors, gate length and the time constant of the RC circuit. Recall that these are the same factors that controlled linearity in the sawtooth generator. The formula developed earlier still remains true and enables us to determine what effect these factors have on linearity. An increase in gate length results in an increase in the number of time constants and an increase in the percentage of charge that the capacitor will take on during this time interval. As stated earlier, if the number of time constants were to exceed 0.1, linearity would decrease. The reason for a decrease in linearity is that a greater percentage of V_{CC} is used. The Universal Time Constant Chart (figure 3-39) shows that the charge line begins to curve. A decrease in gate length has the opposite effect on linearity in that it causes linearity to increase. The reason for this increase is that a smaller number of time constants are used and, in turn, a smaller percentage of the applied V_{CC} is used. Changing the value of resistance or capacitance in the circuit also affects linearity. If the value of C2 or R3 is increased, the time is increased for 1 time constant. An increase in the time for 1TC results in a decrease in the number of time constants required for good linearity. As stated earlier, a decrease in the number of time constants results in an increase in linearity (less than 0.1TC). In addition to an increase in jump voltage (larger value of R3) and a decrease in the amplitude (physical length) of the sawtooth produced by the circuit, electrical length remains the same because the length of the gate was not changed. R2 has a similar effect on linearity because it is in series with R3. As an example, decreasing the value of R2 results in a decrease in linearity. The equation illustrates that by decreasing R (TC = RC), TC decreases and an increase in the number of time constants causes a decrease in linearity. Other effects are an increase in jump voltage and an increase in the amplitude (physical length) of the sawtooth. Changing the value of V_{CC} does not affect linearity. Linearity is dependent on gate length, R, and C. V_{CC} does affect the amplitude of the waveform and the value of jump voltage that is obtained. Q11. For an RC circuit to produce a linear output across the capacitor, the voltage across the capacitor may not exceed what percent of the applied voltage? Q12. Increasing gate length in a sawtooth generator does what to linearity? Q13. In a sawtooth generator, why is the transistor turned on for a longer time than the discharge time of the RC network? Q14. What is added to a sawtooth generator to produce a trapezoidal wave?