VHDL-AMS Hardware Description Language:Frequency-Domain Modeling

Frequency-Domain Modeling

VHDL-AMS supports quiescent, time, and frequency simulation domains identified by the domain signal. The domain signal is set to quiescent domain during the initialization phase of simulation by the simulator. While it is assigned to time domain or frequency domain when the system becomes stable at time zero depending on the kind of simulation we wish to perform.

Time-domain simulation was discussed above. In this section, we deal with the frequency domain. Note that frequency-domain simulation is based on the small-signal model. In this domain, the behavior of a system can be modeled using Laplace- or z-domain transfer functions. The Laplace transform is a continuous transfer function, while z transform is a discrete one.

Several VHDL-AMS models for the high-pass filter of Figure 91.17 are shown in Figure 91.18. The structural model of this filter is shown in Figure 91.18(a). Figure 91.18(b) models the high-pass filter in time domain, while Figure 91.18(c) and Figure 91.18(d) model this filter in frequency domain using Laplace and z transforms, respectively. The latter two models are discussed below.

As shown in Figure 91.18(c), the Laplace transform of a scalar quantity is specified by using the 'ltf attribute. This attribute represents the numerator and denominator polynomials of the corresponding quantity using real_vector arrays. Note that the first element of the denominator array cannot be zero.

where wp = R ´ C . This transfer function is represented by num and den vectors in the model of Figure 91.18(c). In these constants, coefficients of the numerator and denominator polynomials starting with 0 power are presented in ascending order.

The behavior of a continuous object can also be modeled by the z-transform. To approximate the discrete transform of a continuous object, the values of that object must be sampled at discrete times.

VHDL-AMS provides two mechanisms for z-domain modeling. The first mechanism uses 'zoh and 'delayed attributes to perform the sample-and-hold process and the z-domain delay (z -1) implementation. The second method combines the sample-and-hold process and the z-domain delay implementation by using 'ztf attribute [2].

Figure 91.18(d) shows the z-domain model of the high-pass filter shown in Figure 91.17. In this figure, the z transform of the Vi quantity is specified by the 'ztf attribute. The arguments of this attribute represent numerator and denominator polynomials of the corresponding quantity as well as the sampling period. Note that the z-domain transfer function of a circuit is created from its Laplace-domain transfer function by using bilinear transform. Bilinear transform replaces all occurrence of operator S in the given Laplace-domain transfer function with

As before, num and den of Figure 91.18(d) that are used with the 'ztf attribute are real_vector array constants. These arrays represent numerator and denominator coefficients in ascending order.

As discussed, quantities have three categories of free, branch, and source. Free and branch quantities have already been discussed. In this section we will present source quantities. A source quantity is used for response and noise modeling of small-signal spectral in the frequency domain. A spectral source quantity is a stimulus for the frequency-domain simulation. To model a sinusoidal signal of the form A = Am cos(wt+ a), a source quantity can be used. For example, a source quantity representing signal A = 5cos(wt + p/6) is defined as quantity A: real spectrum 5, math_pi/6.0

As shown above, a spectral source quantity represents the magnitude and phase of the related source as well as the type of the quantity values. The value of a spectral source quantity is zero except during frequency-domain simulation.