compare :
An analog clocked comparator.

The compare primitive samples xreal-typed input signals in and in_ref at each rising edge of an xbit-typed input trig and determines whether their difference (i.e., in–in_ref) is higher or lower than the threshold level. In other words, its xbit-typed output out is set to 1 if the difference is higher than the threshold and is set to 0 otherwise. Here the threshold level is defined by the threshold parameter. The primitive can also model random decision errors by specifying a non-zero RMS value of the input-referred noise (noise_in).

The compare primitive can operate in two modes: an ideal comparator model and a finite-aperture comparator model. For the latter mode, the finite sampling aperture of the comparator is modeled by an impulse sensitivity function (ISF).

1) Ideal comparator model

In this mode, the compare primitive models an ideal clocked comparator behavior. In other words, the comparator samples the instantaneous value of the input difference in–in_ref at the rising edge of trig and outputs 1 if the sampled value is higher than the threshold and 0 otherwise.

An input dead zone can be modeled using the sensitivity parameter. In other words, an xbit-typed output out is set to 1 if the input difference value is higher than threshold+sensitivity and is set to 0 if lower than threshold–sensitivity. If the difference is between threshold–sensitivity and threshold+sensitivity, out keeps its previous value.

2) Finite sampling aperture comparator model

A realistic comparator acts on a weighted average of the input signal over a certain finite time window rather than on an instantaneous value of the input at one particular time point. This finite sampling aperture can be described by an impulse sensitivity function (ISF), which describes the comparator’s internal response measured at one chosen observation point (t_obs) to an impulse input arriving at time t.

The finite sampling aperture of most comparators is contributed by two operating phases of the comparator, sampling and regeneration phases. During the sampling phase, the comparator transfers the input signal to its internal node through a finite-bandwidth low-pass filter. The later arriving input has the larger impact to the output, resulting in an ISF whose magnitude decreases as the arrival time t decreases (e.g. left exponential). On the other hand, during the regeneration phase, the signal stored on the internal node grows exponentially over time via a positive feedback. The earlier arriving input has the larger impact to the output, resulting in an ISF whose magnitude decreases as the arrival time t increases (e.g. right exponential).

             ISF(t) measured at the observation time
              ^
              | sampling          regeneration
              | time       .      time
              | constant  / \     constant
              |          /    \
              |         /       \
              | -------/          \----------------
              |-------------------------------------> t

              |----------->| sampling instant

              ||

More description on modeling the finite sampling aperture and noise behavior of clocked comparators can be found in the following publication:

- J. Kim, B. S. Leibowitz, M. Jeeradit, "Simulation and Analysis of Random
  Decision Errors in Clocked Comparators," IEEE Trans. Circuits and Systems I,
  pp 1844-1857, Aug. 2009.

The compare primitive models a typical ISF of the comparator using the following six member parameters listed in the parameter ISF_params:

    ISF_params[0]: sampling instant (time delay to the peak of ISF)
    ISF_params[1]: sampling gain (when t_obs > 0, it refers to the total area of the ISF function)
    ISF_params[2]: sampling time constant (shape of the left exponential)
    ISF_params[3]: regeneration time constant (shape of the right exponential)
    ISF_params[4]: internal latch threshold (determining metastability)
    ISF_params[5]: observation time (t_obs; optional)

When any of ISF_params[0]~ISF_params[4] is negative (e.g., -1), the compare primitive operates in the ideal comparator mode. The interpretation on the sampling gain (=ISF_params[1]) is different depending on the observation time parameter t_obs (=ISF_params[5]). When t_obs <= 0, the sampling gain is simply the scale factor applied to the net input (i.e., in–in_ref–threshold) before it goes through sampling and regeneration. On the other hand, when t_obs > 0, the sampling gain refers to the total area of the ISF function measured at a particular observation time, t_obs. If ISF_params[5] is not specified, it is assumed to be -1.

Input/Output Terminals

Name	I/O	Type	Description
out	output	xbit	digital decision output
in	input	xreal	analog input
in_ref	input	xreal	reference input
trig	input	xbit	trigger input

Parameters

Name	Type	Default	Unit	Description
threshold	real	0.0	None	threshold level
noise_in	real	0.0	None	RMS value of input-referred noise
sensitivity	real	0.0	None	input sensitivity
ISF_params[0]	real	-1.0	seconds	sampling instant
ISF_params[1]	real	-1.0	None	sampling gain
ISF_params[2]	real	-1.0	seconds	sampling time constant
ISF_params[3]	real	-1.0	seconds	regeneration time constant
ISF_params[4]	real	-1.0	None	latch threshold
ISF_params[5]	real	-1.0	seconds	observation time (optional)
delay	real	0.0	seconds	latch delay
init_value	logic	1’bx	None	initial output value
trig_mode	int	1	None	triggering mode

compare :An analog clocked comparator.

1) Ideal comparator model

2) Finite sampling aperture comparator model

compare :
An analog clocked comparator.