WO2006128714A1

WO2006128714A1 - Simulation of electronic circuit behaviour at high frequencies

Info

Publication number: WO2006128714A1
Application number: PCT/EP2006/005264
Authority: WO
Inventors: Thomas Brazil
Original assignee: University College Dublin, National University Of Ireland, Dublin
Priority date: 2005-06-03
Filing date: 2006-06-02
Publication date: 2006-12-07
Also published as: IES20050375A2

Abstract

A method and software component are disclosed for performing simulations of electronic circuit behaviour. The method comprises transforming S-parameters that describe the reflection and transmission coefficients of a circuit to produce a plurality of discrete-time, real-valued impulse response weights and using these response weights in a time domain transient simulation. The transformation may involve the production of intermediate parameters referred to as 'F-parameters', which may be generated in accordance with the formula: Fij (ƒ) = [Sij; (ƒ)- K]e-jωτ , where Sij are the S-parameters that describe the circuit. The values of K and τ are selected such that K and τ comprise real numbers, and τϵ [0,1/(2.ƒm)], where fin is the maximum frequency at which the circuit is to be modelled. K and τ are selected to satisfy the following simultaneous conditions: Condition 1 - Im{Fij(ƒm)} = 0; and Condition 2 - the impulse response weight calculated as a result of Condition (1) at time = 0 is forced to be exactly zero.

Description

SIMULATION OF ELECTRONIC CIRCUIT BEHAVIOUR AT HIGH FREQUENCIES

This invention relates to simulation of the behaviour of electronic circuits. It has specific application to simulation of circuit behaviour using software models.

Many systems have been proposed to simulate the behaviour of electronic circuits so that it is possible for a designer to predict the behaviour of a circuit before it is built and to select the components required to enable the circuit to perform an intended function. For all but the simplest of circuits, the mathematical equations that describe operation of the circuit are too complex to be solvable using analytical mathematics alone. Therefore, it is usual to model circuits using discrete-time numerical methods.

A fundamental and commonly encountered problem in high-frequency simulation is that simulation in the time domain becomes progressively less accurate as frequency increases. Therefore, it becomes necessary to incorporate known frequency-domain data (e.g., scattering parameters, otherwise known as S-parameters) within a time-domain simulation. Many approaches to this problem have been proposed over the years, most commonly involving some kind of rational function approximation (for example, a Pade approximant) to the given data followed by recursive convolution within a time-domain simulation [l]-[m]. However, these approaches suffer from a number of serious drawbacks. The great majority of this work has been directed to the special case of lossy multiple-conductor transmission lines, neglecting other circuits. More fundamentally, they present difficulties with reliable extraction of the polynomial coefficients together with general problems associated with achieving good accuracy under general conditions while also preserving stability and causality.

In principle the task at issue could be performed using the Fourier transform or fast Fourier transform followed by a convolution between the resulting impulse response and the input signal. In practice, this is far from straightforward except in very special cases. A basic problem is that the given data is known only up to the maximum frequency f_m and fairly obvious strategies such as using a 'window' function to kill off the given function outside the known band can create serious inaccuracies. Periodic extension appears attractive but experience has shown that it is very difficult to manage for both reflection and transmission parameters.

An aim of this invention is to provide an alternative approach to this problem, with the more specific aim of representing in the time-domain all of the S-parameters of a completely arbitrary JV-port, linear, time-invariant network that are available up to some maximum frequency of interest /„.

It will be shown how each complex-valued S-parameter can be represented with extremely high frequency-domain accuracy through a special formulation based on a non-uniformly- spaced, compact sequence of discrete-time, real-valued impulse response weights. The resulting representation is easily obtained and is ideally suited to implementation within a linear or non-linear time-domain transient simulator. Several examples are given which validate the accuracy of the frequency-domain representation as well as the accuracy of both transient and steady-state responses in linear and non-linear time-domain simulation. The results also demonstrate exceptional simulation speed, stability and accuracy.

From a first aspect, this invention provides a method of performing circuit simulation comprising transforming S-parameters that describe the reflection and transmission coefficients of a circuit to produce a plurality of discrete-time, real-valued impulse response weights and using these response weights in a time domain transient simulation.

The transformation may involve the production of intermediate parameters referred to as "F- parameters". Such F-parameters may be generated in accordance with the formula:

F_u (/)

, where S_v are the S-parameters that describe the circuit. To achieve an optimum result, the values of K and τ are selected such that K and τ comprise real numbers, and r ε [0, \ /(Lf_n)], where^ is the maximum frequency at which the circuit is to be modelled. Preferably, K and τ are selected to satisfy the following simultaneous conditions: Condition 1 — Im(F_y(Z^) } = 0; and Condition 2 — the impulse response weight calculated as a result of Condition (1) at time = 0 is forced to be exactly zero.

From another aspect, this invention provides a computer software component for use in circuit simulation operative to take as its input a file containing S-parameters that describe a network, transforming the S-parameters to produce as an output, a plurality of discrete-time, real- valued impulse response weights for use in a time domain transient simulation.

Such a software component can act as a front-end to a time-domain simulation application that is capable of interpreting S-parameters. In such embodiments, the output of the front-end is a component model that can be incorporated into an input file for the simulation application. Alternatively, it may be a module of a simulation application.

An embodiment of the invention will now be described in detail, by way of example, and with reference to the accompanying drawings, in which:

Figure 1 is a time-domain representation of a periodic extension of F_l}(j)\

Figure 2 is a time-domain representation of a scattering parameter S_υ(j);

Figure 3 shows an example of a lossy distributed/lumped test network having a stub length θ varied over three values: 11°; 54°; 97°;

Figure 4 illustrates frequency domain behaviour as predicted by time domain description produced by the embodiment compared to the exact response for three different stub lengths in Figure 3 (based on 32 frequency-domain samples);

Figure 5 is a time-domain representation of Sl 1(/) for three line lengths in the circuit of Figure 3;

Figure 6 shows a general linear two-port network for transient analysis, the network being described by an [S] matrix;

Figure 7 presents a comparison between output voltage from convolution-based transient analysis and steady-state (analytical) result, the generator voltage consisting of two 0.1 V tones at 2.0 GHz and 2.7 GHz respectively; Figure 8 is a graph of a small-signal transient analysis of a complete pHEMT matched amplifier (ideal transmission lines), one trace being produced by the embodiment and the other closely aligned trace being produced by a known simulator; and

Figure 9 is a graph of the output of non-linear simulator embodying the invention for the amplifier of Figure 8 at 2GHz and input drive level of 2.5 V.

This embodiment implements the invention in a pre-processing module for a pre-existing software simulation system such as ADS from Agilent or Microwave Office from Applied Wave Research, amongst other possibilities. The module takes as its input S-parameters that describe a network, translates them to the intermediate values, referred to as F-parameters, fulfilling necessary rules (which will be described), and produces values of variables τ and K. The S-parameters are typically provided by manufacturers of an electronic device, that can be "dropped in" to a description of a circuit to be simulated. This embodiment takes such a model as its input and produces a replacement model that can similarly be used in construction of a complete circuit model.

In this embodiment, the main simulation software itself remains unchanged, but is provided with the F-parameters and the values τ and K. The intermediate F-parameters are then transformed into the time domain, and the new time-domain values are used in time-domain simulations having an additional impulse K and shifted by τ, as shown in Figure 2. These are then provided as an input to a time-domain simulation application. It has found that this produces the accurate and stable simulation results, with an efficient use of calculation resources, allowing the incorporation of the frequency-domain data within the time-domain simulation.

In principle the task at issue can be performed using a Fourier Transform or Fast Fourier Transform followed by a convolution between the resulting impulse response and the input signal. In practice, this is far from straightforward except in very special cases. A basic problem is that the given data is known only up to the maximum frequency /„ and fairly obvious strategies such as using a 'window' function to kill off the given function outside the known band can create serious inaccuracies. Periodic extension appears attractive but seems very difficult to manage for both reflection and transmission parameters. Consider now a given Hermitean S-parameter function S_υφ = (S '_tJφ + j.S,_jφ), either reflection or transmission, referred to Go and specified at (N+ 1) equally-spaced tabulated values of/ε [0, Z_nJ with interval Δ/ A direct periodic extension of the given data beyond the known range [-f_m, f_m] will, in general, introduce major complex-valued discontinuities at each boundary frequency. If it were then attempted to convert a function of this kind into the time- domain, the resulting impulse response would be of very long duration and/or would have very poor interpolation properties back into the frequency-domain between the original data points. Consider now the new function:

where K and τ comprise real numbers, and τ ε [0, \/(2.f_m)]. In this embodiment, these numbers satisfy the following two simultaneous conditions:

Condition 1 : lm{F,/f_m)} = 0. For a Hermitean Sij this is sufficient to avoid a discontinuity in F,_j at Fi_j is thus continuous and periodic in a complex-valued sense and may be represented efficiently by a discrete-time sequence of impulse response weights separated by

Condition 2: The impulse response weight calculated as a result of condition (1) at time = 0 is forced to be exactly zero.

The resulting time-domain representation of F_vφ may resemble that shown in Figure 1. However, the objective is to obtain a discrete-time representation of the scattering parameter S_vφ. This is achieved as follows:

(a) Remove the additional phase shift introduced by the exponential term in equation (1), above. This corresponds to shifting the entire response in Figure 1 by an amount τ to the left; that is, in the direction of negative time. This also explains the need for condition (2), since moving the first, zero-valued weight into the negative time region does not then led to a violation of causality. (b) If K is non-zero, introduce an additional impulse at time = 0 of value (K.At_ιr). The discrete-time representation of Syφ is therefore as shown in Figure 2. It is potentially nonuniform adjacent to the origin, it is but uniform otherwise. Typically, the order of 50-100 weights are sufficient to represent even quite complex frequency-domain behaviour.

It can be shown that the procedure required to satisfy simultaneously Conditions (1) and (2) involves determining a value of τ in the range [0, l/(2.f_m)] such that:

Δ/.

where

and ω_m = 2.π.f_m.

This is a straightforward numerical exercise in finding a bracketed root of an algebraic non- linearity.

As an example of the application of this method, consider an arbitrary distributed/lumped linear TPN as depicted in Figure 3.

The transmission lines are highly non-commensurate and further exhibit significant loss and dispersion. To provide a more robust test of the procedure, one of the transmission line lengths is tuned over three separate electrical lengths producing very different frequency- domain responses. Then, starting with 32 frequency-domain samples in the range between DC and 12GHz, the procedure described above was used to compute the time-domain representation for each S-parameter. The results presented in Figures 4a to 4d show the frequency-domain analyses of the original circuit (for the three lengths) using a high resolution in the frequency-domain, compared to the predictions of the kind of time-domain representation shown in Figure 2 for SI l (input reflection coefficient) and S21 (forward transmission coefficient) in terms of both magnitude and phase, respectively in Figures 4a to 4d. S22 (output reflection coefficient) is similar.

The time-domain representation for SI l is also presented in Figure 5 showing a detail of the region near time zero to emphasise the non-uniformity in time of the IR weights in this region for the three cases. It is important to note that these are fully interpolated results: all of the time-domain data records have been augmented with a significant number of zeroes to provide greatly enhanced frequency-domain resolution for the purpose of making these comparisons.

The quality of the time-domain representations in Figure 4 is uniformly excellent. Invariably, smooth, continuous and exceptionally accurate frequency-domain responses are generated between the much smaller number of frequency-domain points that were used for their initial calculation right up to the maximum frequency f_m. Extensive tests using measured S-data, S- parameters from EM simulation or from circuit simulation has repeatedly confirmed that these results are quite typical of what can be achieved with the method described here. Such small errors that do occur tend to be exactly where they are least detrimental: when the magnitude function is anyway very small or else close to the upper frequency limit of representation/_π.

Embodiments of the invention can implement both linear and non-linear transient simulators using the representation of S-parameter data described above. Indeed, the form of discrete- time representation used is very easy to incorporate into such simulators. As an example, consider the particular case shown in Figure 6 where the aim is to simulate the transient terminal voltage responses of a linear two-port network known only though S-parameters when the network is excited at port (1) by a generator V_gen(t) that is switched on at time zero.

A two-tone form is chosen for V_gen{t) as the steady-state response is then easy to determine from standard circuit theory, and provides a useful verification of the asymptotic trajectories of the transient analyses.

To find the transient responses, a method embodying the invention first coverts SI l and S21 into equivalent discrete-time representations using the method described above. Then convolutions are performed involving these discrete-time representations with a time- sampled representation of the generator voltage V_gen(i). The convolutions are especially efficient and simple to perform if the time-step for main impulse response record (and ideally also an approximation to the delay τ) is chosen to be some integer multiple of the time-step At used in the transient analysis. Often this kind of flexibility is available at no particular cost. Although it has been suggested that convolutions of this kind always have to be carried out over the whole past record from time 0, and therefore the computational cost increases quadratically with time, in fact this need not be true. The impulse responses used in this embodiment are strictly limited in duration so the cost is low and bounded, independent of the time at which they are computed.

Figure 7 shows an example of a transient analysis performed in this way. It will be seen that the response is smooth and well-behaved and tends in a steady-state towards a very close agreement with the analytical results, as required.

As a specific verification of the transient potion of the response, a complete pHEMT amplifier with ideal lumped matching networks has been described within a separate commercial transient simulator. This simulator has also been used to derive a table of small- signal S-parameter data for the complete amplifier. This data is then used as the 'S-data block' in Figure 6 and a transient analysis performed as just described. These results can be directly compared with a transient analysis of the original circuit using the commercial simulator, providing a completely independent verification test. The results presented in Figure 8 again show extremely close agreement. Finally, a highly non-linear analysis was performed for the same amplifier with an amplitude of 2.5V. The results shown in Figure 9, when continues for over one million time steps with four convolutions at each time step, took less than 30 seconds on a 1.3GHz PC.

A natural question is what does the form of the representation shown in Figure 2 do outside the frequency range up tof_m for which it was developed. It turns out that it predicts smooth behaviour at higher frequencies but of course the behaviour is generally quite different from that predicted by the original process. Hence f_m should be chosen to be of the order of the highest significant signal spectral component that is of interest, but this is not particularly critical. Generation of very long transient responses with exciting signals both below and well above f_m for a wide variety of test circuits show no evidence of instability. While this embodiment was implemented as a pre-processing module for an existing software simulation application, other implementations are possible. It will be understood that the procedure of generating the F-parameters and the values of K and τ need, in principle, be calculated just once for each device model to produce a transformed model that can be used any number of times in simulation applications. Hence, it is convenient to perform the transformation in a separate pre-processor.

When used with an unaltered simulation application, the pre-processing module must derive the F-parameters from the provided S-parameters satisfying the conditions described above. The module then transforms the S-parameters to the time domain to produce the corresponding impulse response, as shown in Figure 1. This impulse response is then adjusted by the derived values of K and τ to produce a time-domain unit impulse response corresponding to the original S-parameters, as illustrated in Figure 2. This response is then used by the simulator, which is then able to use the pre-generated impulse response to obtain the transient analysis.

Another approach is to incorporate part of the functionality described above into the simulation application itself. This requires adaptation of the simulation application to interpret the parameters K and τ and modify its operation accordingly. The pre-processing module takes the S-parameters as its input, chooses the values of K and τ to fit the specified conditions and creates the corresponding F-parameters. These values of the F-parameters, K and τ are then passed to the adjusted simulator. The simulator operates conventionally to create an impulse response based on the F-parameters. The impulse response is then adjusted using the K and τ values to produce an impulse response corresponding to the original S- parameters (as in Figure 2). This is then stimulated to produce the transient responses (a time-domain signal) of the system to be analysed.

In conclusion, a new and effective general method has been developed for the incorporation of frequency-domain (S-parameter) data into a linear or non-linear time-domain transient simulation, in a way that is easy to implement, very accurate, fast and stable.

Claims

1. A method of performing circuit simulation comprising:

providing S-parameters, S_tJ, that describe the reflection and transmission coefficients of a circuit;

producing intermediate F-parameters, F,_p from said S-parameters, wherein the F- parameters are generated in accordance with the formula: F_y (Z) = [S_y(Z)- ATJe^"-"⁰⁷ and wherein the values of K and τ are selected such that K and τ comprise real numbers, and τ ε [0, 1/(2.Z_J)], where Z_I is the maximum frequency at which the circuit is to be modelled;

producing a plurality of discrete-time, real- valued impulse response weights from said

F-parameters;

shifting said impulse response weights for the circuit in time by the value τ;

adding an impulse K at time value 0 to the impulse response weights; and

using said adjusted response weights in a time domain transient simulation.

2. A method of performing circuit simulation according to claim 1 in which K and τ are selected to satisfy the following simultaneous conditions: Condition 1 ~ Im{F_j,{/^)} = 0; and Condition 2 - the impulse response weight calculated as a result of Condition (1) at time = 0 is forced to be exactly zero.

3. A method according to claim 1 wherein said circuit is band-limited and wherein the value K is complex valued and the impulse response weights are complex valued.

4. A computer program product comprising computer executable code which when executed on a computing device is operable as a circuit simulation application to perform the steps of claim 1.

5. A computer program product according to claim 4 including a front end module operable to output a component model that can be incorporated into a circuit description for use with the circuit simulation application.