KR20030043152A - Method for Signal Verification in Multi-Coupled Transmission Line System - Google Patents

Abstract

PURPOSE: A method for verifying a signal on a transmission line in a wiring system is provided to perform simply an analysis for transformation and noise of signal by using only 3 poles in a frequency region. CONSTITUTION: A plurality of transmission lines are divided into the combination of independent modes in order to express signal formulas for each independent mode by using a modal analysis method(S1). The 3 pole approximation waveform is obtained by approximating the signal formulas for the each independent mode to 3 poles in a frequency region and the 3 pole approximation waveform is converted to a response of a time region(S2). The response of signal is reconstructed by using a linear approximation method and a transformational RC response approximation method(S3). A state of signal on the transmission line is verified by using the reconstructed response of signal(S4).

Description

Method for Signal Verification in Multi-Coupled Transmission Line System

The present invention relates to a signal verification method using a waveform approximation method in a system consisting of a plurality of transmission lines. In particular, the waveform approximation method enables simple and accurate timing, signal delay, crosstalk and overshoot / undershoot values of a signal on a transmission line. It is about a method of verifying the back.

As the operation speed of the recent VLSI (Very Large Scale Integrated Circuit) system and other high-performance systems rapidly increases, the damage, delay, and various noises generated through the signal transmission path not only influence the performance of the entire system, but also enormous design. It is causing an increase in costs.

In particular, wiring in high-performance systems is absolute enough to reach about 80% of system performance, so designing a circuit without verifying the timing, noise, and purity of the correct signal by the wiring can result in significant design costs.

In the related art, an elmore model or a modified RC model was used as a wiring model to verify the timing of signals or to verify crosstalk noise between wirings. In the accompanying drawings, the RC wiring model shown in FIG. Since it is a model that can be used under the assumption that it is governed by, there is a problem that cannot be used in a general network.

In addition, the network analysis method by the known modal analysis method for accurate signal analysis in a large number of common networks includes complex integration calculations, so that the timing of signals on a complicated wiring, timing verification, routing, or complicated wiring requires fast and accurate network analysis. There is a problem that can not be used to verify purity.

Therefore, based on the rational function approximation method, such as AWE (Asymptotic Waveform Approximation), a technique has been developed to approximate the waveform without complex integral calculation using a large number of system poles and zeros, but the AWE method or similar method has a large inductance. Fundamentally, unless you use infinite poles and zeros, including high-frequency poles, you can't reconstruct an accurate waveform, and you have fundamental problems with the stability of the analysis method that the system response waveform emits.

For example, in the case of a wiring system composed of a single transmission line as shown in FIG. ) Is partially lost and reflected when the impedance is inconsistent with the transmission line and reflected the characteristic impedance of the transmission line ( Is the impedance of the source ( If greater than), the electromagnetic wave in the time domain shows a ringing phenomenon.

In addition, the output waveform of the transmission line is a discontinuous point (that is, The abrupt change of the signal is conceptually attached as shown in FIG. Cannot be represented exactly.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and an object thereof is to separate a plurality of transmission lines of a wiring system into independent wiring networks in the frequency domain and obtain a waveform in the time domain without integration for each independent mode in the time domain. By applying linear approximation and modified RC response approximation to the waveform, the response waveform of the entire signal is reconstructed so that the timing, signal delay, crosstalk, and overshoot / undershoot values of the signal can be verified accurately and quickly in the network. To provide a signal verification method on a transmission line in a wiring system.

1 is a view showing an RLC wiring network model of a typical wiring network.

2 is a diagram illustrating an RC network model.

3 shows a single transmission line model.

4 shows a conceptual response waveform in a lossless single transmission line.

5 shows a 3-pole approximation response waveform and an effective flight time.

Fig. 6 shows an RLC circuit model at disconnection.

FIG. 7 shows a 3-pole approximation response at near-end and far-end in FIG. 6.

8 shows response waveforms using the TWA method and HSPICE simulation at disconnection.

9 is a diagram showing 50% signal delay according to transmission line parameter change in disconnection.

10 is a wiring diagram when a branch line is provided.

FIG. 11 is a diagram showing a response waveform using a TWA method and a HSPICE simulation according to a change in the length of an edge in FIG. 10. FIG.

12 is a diagram showing a wiring structure composed of two lines.

13 shows response waveforms using the TWA method and HSPICE simulation in a two-wire structure.

14 is a diagram showing a wiring structure composed of three lines.

FIG. 15 shows response waveforms using the TWA method and HSPICE simulation in FIG. 14; FIG.

Fig. 16 shows a wiring structure composed of five lines.

FIG. 17 shows response waveforms using the TWA method and HSPICE simulation in FIG. 16; FIG.

18 is a flowchart for explaining a signal verification method according to the present invention;

A feature of the present invention for achieving the above object is a signal verification method on a transmission line in a wiring system,

Expressing a signal expression for each independent mode after separating a plurality of transmission lines into a combination of independent modes; Converting the signal equation for each independent mode into three pole approximations in the frequency domain to obtain a three pole approximation waveform and converting the signal equation into a time domain response; Reconstructing the response of the signal by applying a linear approximation method and a modified RC response approximation method from the time domain response of the 3-pole approximation waveform; The method for verifying a signal on a transmission line in a wiring system comprising the step of verifying a state of a signal on the transmission line through the reconstructed response.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The present invention provides a method for verifying the state of a signal, that is, timing, signal delay, crosstalk, and overshoot / undershoot values in a wiring system composed of one or more transmission lines. The waveform approximation method (TWA) in a wiring system composed of a single transmission line is described.

The system function of a wiring system composed of a single transmission line in the frequency domain may be expressed as Equation 1 below.

Here, the reflection coefficient of the source stage and the reflection coefficient of the load stage are respectively Propagation constant, characteristic impedance and load impedance are respectively to be. Equation 1 may be expressed as Equation 2 below in the far-end (x = l) of the transmission line,

In the near-end of the transmission line (x = 0) it can be expressed as shown in Equation 3 below.

Thus, the three-pole approximation function ) Can be expressed as Equation 4 below.

here, Is a constant.

On the other hand, the 3-pole approximation function ) Can be approximated as in Equation 5 below.

here, Wow Is a constant. Therefore, the three-pole approximation waveform in the frequency domain as described above may be represented by the voltage equation of Equation 6

By Fourier transforming Equation 6, an expression in a time domain as shown in Equation 7 can be obtained.

As described above, the 3-pole approximation waveform in the frequency domain can be easily converted into the time domain without complicated integral calculation. However, since the three-pole approximation waveform is a waveform represented using a finite number of poles, it is not an accurate waveform. Therefore, in order to obtain an accurate response waveform, the waveform approximation method (TWA), that is, the linear approximation and the modified RC response to the three-pole approximation waveform in the time domain, are obtained. Repeat the approximation method to find the exact approximate response waveform.

First, the linear approximation will be described. The linear approximation refers to a method of linearly approximating the waveform of a signal in a section in which reflection can be assumed from the moment the signal arrives at the load.

That is, a function value of the three-pole approximation waveform corresponding to the time at which the signal is reflected from the load from the above-described three-pole approximation waveform in the time domain, that is, the odd times (2n-1) of the signal's flight time, is obtained. This is a method of linearly approximating the waveform of a signal in a given section based on the function value of the 3-pole approximation waveform.

Next, the modified RC response approximation method describes the waveform characteristics that are similar to the RC response waveform because the time interval from the completion of the signal reflection until the next linear approximation is applied is a mechanism in which charge and discharge are dominant. However, because the inductance effect is included and the final value is different and the effective charging time is modified, a method of describing a signal characteristic corresponding thereto is called a modified RC response approximation method.

The above-described linear approximation and modified RC response approximation will be described in detail with reference to the accompanying drawings.

First, with respect to the three-pole approximation waveform, which has been transformed into the time domain, the flight time of the incident wave, After calculating, the effective flight time considering the load, When the time difference is expressed as in Equation 8 below.

here, Is the total inductance of the wiring Is the total capacitance of the wiring Is the load capacitance. The effective flight time can be shown as shown in FIG. Reach the load in time and It has the property that reflection is completed in time. Where n is the reflected count value and is a positive integer. That is, the incident wave It causes sudden waveform changes over time. This sudden change in signal is due to the large reflection coefficient of the load. On the time axis to be twice the value of the function in and The time interval between can be approximated by a linear function.

Also, since the reflected waveform changes with the characteristics of charging or discharging of monotonically increasing or monotonically decreasing until the next discontinuity point of the load, the time domain and In the interval between, the waveform is similar to the RC response.

Thus, the stomach and In the time domain between, we can express it using modified RC response approximation. In this case, the effective time constant of the response function may be expressed by Equation 9 below.

The waveform approximation in the RC-type transmission line far-end using the effective time constant of the above response function can be represented using a modified RC model as shown in Equation 10 below.

here, ego

to be.

In a similar manner, the waveform approximation at the transmission line approximation may be represented by a modified RC model as shown in Equation 11 below.

here silver

to be.

As described above, the waveform approximation method for a single transmission line can be extended to a case where a plurality of transmission lines are coupled to each other.

As shown in FIG. 1, a wire network in which n wires are electrically coupled to each other may be assumed to transmit electromagnetic waves in a TEM mode. In this case, a mathematical expression of a signal may be represented by Equation 12 below. .

Here, [Z] and [Y] are the determinants of the series impedance and the parallel admittance of the transmission line, respectively, and these parametric determinants can be expressed as Equation 13 below using the electrical circuit model parameters of the wiring.

Here, [R] is a resistance matrix per unit length (hereinafter referred to as PUL), [L] is a PUL inductance matrix, [G] is a PUL conductance matrix, and [C] is a PUL capacitance matrix.

On the other hand, using the equation (12) can be expressed as the following equation (14) if only the voltage in the transmission line expression.

Equation 14 is The eigenvalues of the determinant may be used to represent the eigenvalues. The characteristic eigen matrix corresponding to the system eigenvalues is represented by Equation 15 below.

here, Is the column vector corresponding to the i th eigenvalue and the system eigenvalue can be found using the similiarity transform.

Once the eigen matrix is obtained, the voltage equation can be re-expressed using eigenvalues and eigen matrix equations as shown in Equation 16 below.

Here, [E (x)] is a diagonal matrix as shown in Equation 17 below.

Of equation (16) and Is a constant vector that can be determined by boundary conditions. In addition, the electric circuit model value for the modal basis vector may be calculated using the determinant of Equation 18 as follows.

Once the voltage equations have been completely separated into mode basis vectors, the waveform approximation method (TWA), as with a single transmission line, for each of these modes can be used to approximate the waveform at the near and far ends of all wiring.

Next, various embodiments of the waveform approximation method described above will be described with reference to the accompanying drawings.

First, in the case of the single transmission line as shown in FIG. 3, an equivalent circuit model is shown in FIG. 6, and transmission line parameters are shown in Table 1 below. Table 1 below shows transmission line parameters of RLC wirings with oxide thickness '2.0' [um], wiring thickness '1.2' [um], silicon substrate thickness '298' [um] and wiring length '1' [cm]. .

Width [um] 0.8 179.6 14.296 0.966 0 One 30 0.5 50 0.1 1.0 143.7 13.851 1.035 0 One 30 0.5 50 0.1 1.6 89.8 12.913 1.151 0 One 30 0.5 50 0.1 2.0 71.8 12.468 1.228 0 One 30 0.5 50 0.1 5.0 28.7 10.645 1.808 0 One 30 0.5 50 0.1 10.0 14.4 9.276 2.776 0 One 30 0.5 50 0.1

Therefore, for the equivalent model of FIG. 6, the 3-pole approximation response waveform is shown in FIG. 7. In this case, Equation 2 and Equation 10 are represented at the far end, and Equations 3 and 11 are approximated at the far end. An approximate waveform can be obtained by applying to the HSPICE simulation result, as shown in FIG. 8 showing the HSPICE simulation value and the result obtained by the waveform approximation method at the near end and the far end of a single transmission line. It is almost coincident with.

In the waveform approximation method, 50% for verifying the timing of the digital circuit is calculated by substituting '0.5' in the voltage equations represented by Equations 10 and 11 for a single transmission line and expressing it in terms of time. The signal delay value can be calculated mathematically.

That is, the output voltage waveform ( ) Is a linear interval Is expressed as the following equation

Modified RC Response Interval In the following equation can be expressed.

here, ego

to be.

In order to find the 50% signal delay, Then set n = 1 to find the function value for time. In this case, the signal delay value may be in the linear section or the modified RC response section, so if the 50% value of the final value is in the linear approximation section, the value obtained from the linear approximation function is selected. Select the value obtained from as the delay value.

For example, if the signal delay is in a linear approximation period, i.e. Back side

If the signal delay is in the modified RC response approximation period, i.e. Back side

to be.

9 is a diagram illustrating signal delay values and HSPICE simulation values calculated by the waveform approximation method.

In addition, in the case of a system having multiple branch lines as shown in FIG. 10, the effective flight time of the trunk line with the multiple branches, May be defined by Equation 19 below.

here, Is the flight time of the i branch Means the effective flight time of the branch line with the maximum round trip time of all branches. In addition, '*' used in the superscript means an edge having a plurality of branch lines. Therefore, the approximate waveform to which the waveform approximation method is applied to the edges has the effective flight time. It can be found in the same way as when there is no branch line using. FIG. 11 is a diagram illustrating approximated waveforms and HSPICE simulation values at edges obtained by the waveform approximation method.

Furthermore, in a system composed of two identical transmission lines as shown in FIG. 12, when the unit step function is input to one transmission line and no signal is input to the other transmission line, the mode basis function is expressed by Equation 20 below. Is expressed.

here, ego, to be. Therefore, the voltage signal at the transmission line to which the unit step function is input is divided into two modes as shown in Equation 21 below.

In addition, the voltage signal in the transmission line to which no signal is input is divided into two modes as shown in Equation 22 below.

Therefore, the mode parameter in each wiring can be expressed by the following equation (23),

Transmission line parameters in the system as shown in FIG.

Therefore, by using these values to obtain the response by the waveform approximation method for each eigenmode and linearly combining these waveforms, the response waveform in the system consisting of two lines can be obtained. 13 is a diagram illustrating response waveforms and HSPICE simulation values obtained by a waveform approximation method in a wiring system composed of two lines.

And, in the wiring system consisting of three transmission lines as shown in Figure 14 attached to each independent transmission line after separating in an independent mode as in the wiring system consisting of the two transmission lines described above using equations (14) to (18). By linearly combining the waveform approximation method by the modal basis basis for the angular mode basis, the response waveform of the system consisting of three lines can be obtained.

In this case, the transmission line parameter

to be.

15 is a diagram illustrating response waveforms and HSPICE simulation values obtained by a waveform approximation method in a wiring system including three transmission lines.

In addition, even in a wiring system composed of five transmission lines as shown in FIG. 16, a response waveform can be obtained by using the above-described equations (14) to (18), in which case the transmission line parameters are as follows.

17 is a diagram illustrating response waveforms and HSPICE simulation values obtained by a waveform approximation method in a wiring system including five transmission lines.

Next, an overshoot and undershoot value using the waveform approximation method will be described.

Overshoot and undershoot refer to the positive and negative peaks of the response waveform. Means a function value of the approximate response waveform at, in Is the first overshoot value and when n = 3 when Is the first undershoot value, the second overshoot value when n = 4, and the second undershoot value when n = 5, so that overshoot and undershoot can be obtained by increasing n.

A signal verification method on a transmission line in the aforementioned wiring system will be described with reference to FIG. 18 as follows.

First, a modal analysis method is applied to a wiring system composed of a plurality of transmission lines, separated into a combination of independent modes, and then a signal expression for each independent mode is expressed (step S1).

Then, the approximation function in the frequency domain using the 3-pole signal expression for each independent mode is obtained, and the 3-pole approximation waveform in the time domain is obtained through Fourier transform (step S2).

Then, in the linear approximation section and the modified RC response approximation section, the linear response method and the modified RC response approximation method are applied to reconstruct the entire response waveform (step S3), and the state of the signal from the reconstructed total response waveform, that is, timing, signal The delay, crosstalk and overshoot / undershoot values are verified (step S4).

In addition, the embodiment according to the present invention is not limited to the above, and can be implemented by various alternatives, modifications, and changes within the scope obvious to those skilled in the art with respect to the present invention, in particular, wiring It can be used for network analysis, related CAD tools or network design of semiconductor circuits, multi chip modules (MCM), printed circuit boards (PCBs), electronic packages and other electronic systems that require performance evaluation.

As described above, the present invention enables simple and accurate analysis of signal deformation and noise in a wiring system composed of single line or multiple transmission lines without integrating calculation and approximation using only three poles in the frequency domain. Can be interpreted without fitting.

In addition, since all waveforms in the time domain are represented by analytical equations, a 50% signal delay can be calculated by a simple calculation, and the waveform approximation method according to the present invention is a stable method that does not occur in any case. .

Claims (11)

In the signal verification method on the transmission line in the wiring system, (A) expressing a signal expression for each independent mode after separating a plurality of transmission lines into a combination of independent modes; (B) converting a signal expression for each independent mode into three pole approximations in the frequency domain to obtain a three pole approximation waveform and then converting the signal equation into a time domain response; (C) reconstructing the response of the signal by applying a linear approximation method and a modified RC response approximation method to the time domain response to the three-pole approximation waveform; And (d) verifying a signal state on the transmission line through a response of the reconstructed signal. The method of claim 1, 3-pole approximation waveform in the frequency domain of step (b) ) Is a response function of a frequency domain at the far end of a transmission line as follows. . (here, Is a constant, Paul) The method of claim 1, 3-pole approximation waveform in the frequency domain of step (b) ) Is a response function of the frequency domain at the near end of the transmission line as follows. (here, Wow Is a constant, Paul) The method of claim 1, The linear approximation of the step (c) is the time of flight of the incident wave with respect to the time domain response of the three-pole approximation waveform. ) And valid flight time ( Time after which the incident wave reaches the load And the time when reflection is complete And a time domain response of the three-pole approximation waveform is approximated by a linear function in the interval between the two lines. (here, Total inductance of silver wiring, Total capacitance of the wiring, Is the load capacitance) The method of claim 1, In the modified RC response approximation method of the process (c), the flight time of the incident wave in the time domain response of the three-pole approximation waveform ) And valid flight time ( ), And the time when reflection is complete And time to reach next load After calculating the effective time constant of the response function using the characteristics of the transmission line reflection waveform that monotonically increases or monotonically decreases in the interval between and 3. A method for verifying a signal on a transmission line in a wiring system, characterized in that it approximates the time domain response of the 3-pole approximation waveform in the time interval between. (here, Total inductance of silver wiring, Total capacitance of the wiring, Silver Load Capacitance) The method according to claim 4 or 5, The effective flight time is a valid flight time for a trunk line having a plurality of branch lines as follows in a wiring system having a plurality of branch lines. . (here, Is the flight time of the i branching line, Is the effective flight time of the branch line with the maximum round trip time of all branches, and the superscript '*' is the trunk with multiple branch lines) The method of claim 5, The effective time constant ( ) Is a signal verification method on a transmission line in a wiring system characterized by the following. . (here, Total resistance of silver wiring, Total capacitance of the wiring, Is the load capacitance) The method of claim 5, The effective time constant ( To approximate the time-domain response of the 3-pole approximation waveform, and The time domain response of the 3-pole approximation waveform in the time interval between ) And near-end ( A method of verifying a signal on a transmission line in a wiring system, characterized by approximating the modified RC model in . (here, , , Is the flight time of the incident wave, Is the effective flight time of the incident wave, Is the effective time constant) (here silver ) The method of claim 1, The signal state verification of the step (d) is a linear section, each of which is the time when the incident wave reaches the load and the reflection is completed. Output voltage at )or, Modified RC response interval, which is the time the reflected wave reaches the next load Output voltage at A delay time of the signal is calculated by assuming a corresponding signal delay function value, and then the delay of the signal is verified by selecting a value obtained from the output voltage corresponding to the time interval to which the delay time belongs as a signal delay time. Signal verification method on transmission line in wiring system. (here, , Is the flight time of the incident wave, Is the effective flight time of the incident wave, Is the effective time constant ) The method according to claim 1 or 9, The signal state verification of the step (d) is the output voltage ( Value representing the discontinuity in The overshoot value and undershoot value of the load side are obtained by substituting for the signal verification method on the transmission line in the wiring system. The method according to claim 1 or 9, The signal state verification of the step (d) is the output voltage ( Value representing the discontinuity in The method of verifying a signal on a transmission line in a wiring system, wherein the maximum crosstalk value at the near end and the far end of the transmission line is obtained by substituting a.