The transport delay td can be either constant (typical case) or vary as a function of time (when maxdelay is defined). A time-dependent transport delay is shown in Figure 4-4, with a ramp input to the absdelay operator for both positive and negative changes in the transport delay td and a maxdelay of 5.

Figure 4-4: Transport delay example

From time 0 until 2s, the output remains at input(0). With a delay of 2s, the output then starts tracking input(t - 2). At 3s, the transport delay changes from 2s to 4s, switching the output back to input(0), since input(max(t-td,0)) returns 0. The output remains at this level until 4s when it once again starts tracking the input from t = 0. At 5s the transport delay goes to 1s and the output correspondingly jumps from its current value to the value defined by input(t - 1).

4.5.8 Transition filter

transition() smooths out piecewise constant waveforms. The transition filter is used to imitate transitions and delays on digital signals (for non-piecewise constant signals, see 4.5.9). This function provides controlled transitions between discrete signal levels by setting the rise time and fall time of signal transitions, as shown in Figure 4-5.

Figure 4-5: Transition filter example

transition() stretches instantaneous changes in signals over a finite amount of time and can delay the transitions, as shown in Figure 4-6.

Input to transition filter

Response of transition filter with transition times specified

Figure 4-6: Shifting the transition filter

The general form of the transition() filter is

transition ( expr [ , td [ , rise_time [ , fall_time [ , time_tol ] ] ] ] )

The input expression is expected to evaluate over time to a piecewise constant waveform. When applied, transition() forces all positive transitions of expr to occur over rise_time and all negative transitions to occur in fall_time (after an initial delay of td). Thus, td models transport delay and rise_time and fall_time model inertial delay.

transition() returns a real number which describes a piecewise linear function over time. The transition function causes the simulator to place time-points at both corners of a transition. If time_tol is not specified, the transition function causes the simulator to assure each transition is adequately resolved.

td, rise_time, fall_time, and time_tol are optional, but if specified shall be non-negative. If td is not specified, it is taken to be zero (0.0). If only a positive rise_time value is specified, the simulator uses it for both rise and fall times. If neither rise_time nor fall_time are specified or are equal to zero (0.0), the rise and fall time default to the value defined by ‘default_transition.

If ‘default_transition is not specified the default behavior approximates the ideal behavior of a zero-duration transition. Forcing a zero-duration transition is undesirable because it could cause convergence problems. Instead, a negligible, but non-zero, transition time is used. The small non-zero transition time allows the simulator to shrink the timestep small enough so a smooth transition occurs and any convergence problems are avoided. The simulator does not force a time point at the trailing corner of a transition to avoid causing the simulator to take very small time steps, which would result in poor performance.

In DC analysis, transition() passes the value of the expr directly to its output. The transition filter is designed to smooth out piecewise constant waveforms. When applied to waveforms which vary smoothly, the simulation results are generally unsatisfactory. In addition, applying the transition function to a continuously varying waveform can cause the simulator to run slowly. Use transition() for discrete signals and slew() (see 4.5.9) for continuous signals.

If interrupted on a rising transition, transition() tries to complete the transition in the specified time.

—If the new final value level is below the value level at the point of the interruption (the current value), transition() uses the old destination as the origin.

—If the new destination is above the current level, the first origin is retained.

output_expression(t)

New destination tr

tf

Interruption

Figure 4-7: Completing the transition

Figure 4-7 shows a rising transition is interrupted near its midpoint and the new destination level of the value below the current value. For the new origin and destination, transition() computes the slope which completes the transition from the origin (not the current value) in the specified transition time. It then uses the computed slope to transition from the current value to the new destination.

With different delays, it is possible for a new transition to be specified before a previously specified transition starts. The transition function handles this by deleting any transitions which would follow a newly scheduled transition. A transition function can have an arbitrary number of transitions pending. A transition function can be used in this way to implement transport delay for discrete-valued signals.

Because the transition function can not be linearized in general, it is not possible to accurately represent a transition function in AC analysis. The AC transfer function is approximately modeled as having unity transmission for all frequencies in all situations. Because the transition function is intended to handle dis- crete-valued signals, the small signals present in AC analysis rarely reach transition functions. As a result, the approximation used is generally sufficient.

Example 1 — QAM modulator

In this example, the transition function is used to control the rate of change of the modulation signal in a QAM modulator.

module qam16(out, in);

parameter freq=1.0, ampl=1.0, dly=0, ttime=1.0/freq; input [0:4] in;

output out; electrical [0:4] in; electrical out;

real x, y, thresh; integer row, col;

analog begin

row = 2*(V(in[3]) > thresh) + (V(in[2]) > thresh); col = 2*(V(in[1]) > thresh) + (V(in[0]) > thresh); x = transition(row - 1.5, dly, ttime);

y = transition(col - 1.5, dly, ttime); V(out) <+ ampl*x*cos(2*‘M_PI*freq*$abstime)

+ ampl*y*sin(2*‘M_PI*freq*$abstime); $bound_step(0.1/freq);

end endmodule

Example 2 — A/D converter

In this example, an analog behavioral N-bit analog to digital converter, demonstrates the ability of the transition function to handle vectors.

module adc(in, clk, out);

parameter bits = 8, fullscale = 1.0, dly = 0, ttime = 10n; input in, clk;

output [0:bits-1] out; electrical in, clk; electrical [0:bits-1] out; real sample, thresh; integer result[0:bits-1]; genvar i;

analog begin

@(cross(V(clk)-2.5, +1)) begin sample = V(in);

thresh = fullscale/2.0;

for (i = bits - 1; i >= 0; i = i - 1) begin if (sample > thresh) begin

result[i] = 1.0;

sample = sample - thresh; end

else begin result[i] = 0.0;

end

sample = 2.0*sample; end

end

for (i = 0; i < bits; i = i + 1) begin

V(out[i]) <+ transition(result[i], dly, ttime); end

end endmodule

4.5.9 Slew filter

The slew analog operator bounds the rate of change (slope) of the waveform. A typical use for slew() is generating continuous signals from piecewise continuous signals. (For discrete-valued signals, see 4.5.8.) The general form is

slew ( expr [ , max_pos_slew_rate [ , max_neg_slew_rate ] ] )

When applied, slew() forces all transitions of expr faster than max_pos_slew_rate to change at max_pos_slew_rate rate for positive transitions and limits negative transitions to max_neg_slew_rate rate as shown in Figure 4-8.