KR100871018B1 - Method of Circuit Modeling for Printed Circuit Board - Google Patents

Abstract

The present invention relates to a circuit modeling method of a printed circuit board free of the addition of ports, reducing the calculation time of power / ground plate characteristics, and suitable for high frequency characteristics.

High Frequency, S Parameters, Skin Effects

Description

Circuit Modeling Method for Printed Circuit Boards {Method of Circuit Modeling for Printed Circuit Board}

1 is a diagram illustrating a method of dividing a printed circuit board for modeling a circuit.

2 shows an equivalent circuit of the cell modeled by FIG.

3 is a diagram illustrating a circuit modeling method of a printed circuit board according to an exemplary embodiment of the present invention.

4 to 7 show a method for measuring the dielectric constant of an insulator.

8 is a view showing a change in resistance value with frequency.

9 is a diagram showing a change in resistance value according to frequency according to a rate at which the resistance increases.

10 and 11 are diagrams comparing S parameters by a circuit modeling method of a printed circuit board according to an exemplary embodiment of the present disclosure, S parameters according to the prior art, and actual measured S parameters.

<Explanation of symbols for the main parts of the drawings>

2, 102: node 6, 106: power plane

8, 108: ground plane 10, 110, 114: insulator

104a, 104b: Cell 112: Solder Resist

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a circuit modeling method of a printed circuit board. More particularly, the present invention relates to a circuit modeling method of a printed circuit board suitable for high frequency characteristics.

As the integration density and operating frequency of an integrated circuit increase, simultaneous switching noise (SSN) of an input / output buffer and a core logic of an integrated circuit semiconductor causes serious problems such as signal glitch, timing error, jitter, and logic error.

This simultaneous switching noise is generated at the power / ground of the printed circuit board and must be managed within 5-10% of the reference voltage.

In general, a printed circuit board in which power planes and ground planes are stacked on both sides of a package's power / ground plate, that is, an insulator, is printed circuit using a three-dimensional field analyzer (or 2.5-dimensional field analyzer). After dividing the board into small pieces, the E and H fields were calculated for each piece, and the high frequency characteristics were extracted using the S parameter to form a circuit model. The circuit model was simulated to evaluate the simultaneous switching noise.

However, the method using the field-analyzer not only requires a high-performance computer but also requires a lot of computation time.

In addition, the method using the field-analyzer has a problem that the simulation process must be repeated again when a part to know the circuit characteristics is added, that is, when a port is added.

Accordingly, as shown in FIG. 1, the power / ground plate is divided into a net shape, and the divided pieces are converted into a transmission line, that is, a resistor (R), an inductor (L), a capacitor (C), and a conductance (G). A method of circuit modeling a ground plate is presented.

1 is a view showing a circuit modeling method of a printed circuit board according to the prior art.

Referring to FIG. 1, a circuit modeling method of a printed circuit board according to the related art includes a printed circuit board in which a ground plane 8 and a power plane 6 are stacked on both surfaces of an insulator 10. Divide into nets so that one side has the same size. At this time, the printed circuit board is divided into a net form so as to be less than 1/10 of the wavelength with respect to the frequency of interest of the printed circuit board. Here, the frequency of interest means an operating frequency for operating the printed circuit board and a frequency of an integer multiple thereof.

As shown in FIG. 1 (b), the nodes 2 are formed in the divided portions when the printed circuit board is divided into a net shape, and a cell is formed between each node 2 and the node 2. In each cell, the resistance (R), inductor (L), and capacitor (C) are determined according to the size of the insulator, the dielectric constant, and the size of the conductor.

At this time, one of the cells located at the edge of the printed circuit board is set to a half cell (half cell), the remaining cells except the half cell is set to a full cell (full cell).

After setting each cell, the values of the resistors (R), inductors (L), and capacitors (C) are determined according to the size and dielectric constant of the insulator (10), and the size of the ground plane (8) and the power plane (6). After setting, each cell is converted into an equivalent circuit including a resistor (R), an inductor (L), and a capacitor (C). Here, the equivalent circuit of the cell is formed considering only one frequency.

In this case, the resistor and inductor of the half cell are formed to have twice the size of the resistor and inductor of the full cell, and the capacitor of the half cell is formed to have the capacity of half of the capacitor of the full cell.

However, such a circuit modeling method of the conventional printed circuit board has a problem in that it does not reflect the skin effect or the like because a circuit model is formed for one frequency.

In addition, the circuit modeling method of the conventional printed circuit board has a problem that does not properly reflect the phenomenon at high frequency because the circuit model is formed for one frequency.

Accordingly, the present invention provides a circuit modeling method of a printed circuit board free of the addition of ports, reducing the calculation time of power / ground plate characteristics, and suitable for high frequency characteristics.

In order to achieve the above object, a circuit modeling method of a printed circuit board according to an embodiment of the present invention is a) less than 1/10 of the wavelength to the frequency of interest for a printed circuit board laminated with both the ground plane and power plane on both sides of the insulator Dividing into a matrix form; And b) n inductors having different inductances in series according to the frequency of the cells between the nodes where the divided portions meet, and n + 1 resistors are connected in parallel across the n inductors. An external inductor and a first capacitor are connected in series between one side of the first resistor of the resistor and the common terminal of the first inductor of the inductor and the ground, and between the other side of the first resistor which is the common terminal of the n + 1 resistors and the ground. And modeling the second capacitor as a circuit connected in series.

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

3 is a diagram illustrating a circuit modeling method of a printed circuit board according to an exemplary embodiment of the present invention.

Referring to FIG. 3, a circuit modeling method of a printed circuit board according to an exemplary embodiment of the present invention uses a printed circuit board having a ground plane 108 and a power plane 106 stacked on both sides of an insulator to have a wavelength of interest for a frequency of interest. Partition into one matrix with one side equal to or less than / 10.

When the printed circuit board is partitioned into a matrix, nodes 102 are formed in the partitioned portions, cells 104a and 104b are formed between the nodes 102 and 102, and the cells 104a and 104b are formed. The cells formed at the edges of the printed circuit board are set to the full cells 104b except for the half cells 104a and the half cells 104a.

In this case, the cells 104a and 104b are modeled as a circuit including a resistor, an inductor, and a capacitor, and the outer portions of the power plane 106 and the ground plane 108 are formed in a circular shape as shown in FIG. In order to reflect the skin effect (skin effect) generated by the current flow, it is modeled by considering a plurality of frequencies.

To this end, each cell (104a, 104b) is a ladder form a plurality of resistors (R1, R2, R3, R4) and inductors (L1, L2, L3) according to each frequency in order to analyze the characteristics according to a plurality of frequencies Leads to. In addition, each cell 104a, 104b has a capacitor C / 4 formed at both ends of the cell to represent the capacitor characteristics at node 102.

In other words, each of the cells 104a and 104b has three inductors L1, L2 and L3 having inductances different in frequency according to frequency as shown in FIG. Four resistors R1, R2, R3, and R4 having different resistance values according to frequency are connected in parallel at both ends of L1, L2, and L3, one side of the first resistor R1 and the first inductor L1. An external inductor (L _ext ) and a first capacitor (C / 4) are connected in series between the common terminal of the terminal and ground, and four resistors (R1, R2, R3, and R4) of the first resistor (R1) are connected in common. It is modeled as a circuit in which the second capacitor C / 4 is connected between the other side and ground.

In this case, the inductor and the resistance of the frequency is limited to three and four, respectively, but this can be changed according to the characteristics of the frequency to be measured.

In other words, inductors and resistors may be configured as n and n + 1, respectively, depending on the frequency to be measured.

At this time, the resistance, the inductor and the external inductor of the half cell 104a of each of the cells 104a and 104b have twice the size of the resistance, the inductor and the external inductor of the full cell 104b, and the half cell 104a The capacitor of has a capacity of 1/2 of the capacitor capacity of the full cell 104b.

Here, the sizes of the resistors, inductors, and capacitors are determined according to the size and dielectric constant of the insulator 110 and the distance between the ground plane 108 and the power plane 106.

In addition, the resistors R1, R2, R3, and R4 have a larger value toward the edges in the circular shaped wire shown in FIG. 3A, and the inductors L1, L2, and L3 have smaller values toward the edges. .

This is because the higher the frequency, the greater the inductance from the circular conductor to the edge.

In this case, the conductive lines mean power plane 106 and / or ground plane 108.

Referring to the method of measuring the characteristics of the printed circuit board by measuring the S parameters of the printed circuit board using the circuit modeling of the printed circuit board as follows.

First, the resistors R1, R2, R3, and R4, the inductors L1, L2, and L3, the external inductor L _ext , and the capacitor C / 4 of FIG. 3B are represented by Equations 1 to 5 below. Is set by.

,

,

Here, ξ _R is a value representing the rate at which the resistance increases.

The ξ _R has a different value depending on the conductivity and shape of the conductor, and the optimal value can be derived by comparing the resistance value extracted through a measuring device, for example, a VNA (Vector Network Analyzer), and measuring the ξ _R. The method will be described later.

As disclosed in Equation 1, the resistance has a larger value toward the edge in a circular conductive line.

,

,

,

,

,

,

,

,

,

,

Where ξ _L is the rate at which the inductor grows, σ is the conductivity of the conductor, t ₁ and t ₂ are the thickness of the conductor, δ _hf is the surface thickness for the maximum frequency at the frequency of interest, and δ _x is the resistance change constant depending on the metal roughness. Where L _lf ^internal is the internal inductor for low frequencies, L _lf ^total is the total inductor for low frequencies, and L _hf ^extenal is the external inductor for high frequencies.

In this case, the inductor has a different value according to the conductivity and shape of the conductive wire, and has a smaller value toward the edge of the circular conductive wire.

In addition, t ₁ and t ₂ may be measured by using a microscope after cutting the printed circuit board, and δ _x may be obtained through TDR (Time Domain Reflectometer) / TDT (Time Domain Transmission) and VNA measurements.

Here, the measuring method of δ _x will be described later.

In addition, L _lf ^internal and α _L change with frequency, and L _hf ^extenal has a constant value regardless of frequency.

,

,

,

,

Where ε _r is the dielectric constant of the insulator, d is the thickness of the insulator, t is the average value of t ₁ and t ₂ , l is the horizontal size of the cell, w is the vertical size of the cell, and μ is the permeability.

At this time, d can be measured by using a microscope after cutting the substrate, ε _r can be obtained through TDR / TDT and VNA measurement as shown in Figures 4 to 7.

Looking at the measurement method of ε _r , first, by designing a microstrip line of the structure as shown in Figs. 4 and 5 and measuring the propagation time of the wave by TDT method, by substituting the measured propagation time into The effective ε _r value can be measured.

In this case, when measuring the ε _r value of the insulator 110, for example, FR-4 epoxy, except for the solder resist 112 protecting the power plane 106, a commercial field analyzer is used as shown in FIG. 5. As shown in FIG. 6, the capacitance value of the printed circuit board including the solder resist 112 and the FR-4 is compared with the capacitance value of the printed circuit board formed of one insulator 114 as shown in FIG. 6. ) Ε _r can be extracted.

Where t _f is the wave propagation time, C is the speed of light, and l is the length of the microstrip line.

In addition, δ _x and ξ _R can be extracted from the resistance value for each frequency.

First, using a VNA to a length of another micro-strip line as shown in Figure 4 in order to extract the δ _x value measures the S ₁₁ and S ₂₁ values. In this case, when the measured values of S ₁₁ and S ₂₁ are substituted into Equations 7 to 10, resistance values according to frequencies may be obtained as shown in FIG. 8.

In this case, after determining a frequency outside the skin effect (the boundary between Region 1 and Region 2 in FIG. 8) where the resistance value is represented by Equation 10 from FIG. 8, the determined frequency is substituted into Equation 11, and the value δ _x close to the measured value. Set.

Also, ξ _R value and extracts the the closest ξ _R value and the measured value while changing the value ξ _R as shown in Figure 9 from the circuit model shown in Fig.

,

,

10 and 11 are diagrams comparing S parameters by a circuit modeling method of a printed circuit board according to an exemplary embodiment of the present disclosure, S parameters according to the prior art, and actual measured S parameters.

As shown in FIGS. 10 and 11, the S parameter value by the circuit modeling method of the printed circuit board according to the exemplary embodiment of the present invention is more consistent with the S parameter actually measured than the S parameter value according to the conventional transmission line. Can be seen.

As described above, the circuit modeling method of the printed circuit board according to the embodiment of the present invention forms a circuit model for each cell by forming a ladder and a resistor and an inductor according to frequency in consideration of the skin effect to form a power plane on both sides of the insulator. And it is possible to reduce the calculation time for calculating the characteristics of the printed circuit board laminated the ground plane.

In addition, in the circuit modeling method of a printed circuit board according to an embodiment of the present invention, a port is added to a portion to be measured by forming a circuit model for each cell by forming a ladder and an inductor according to frequency in consideration of a skin effect. Even if it is possible to calculate the characteristics of the part to know the circuit characteristics without recalculation process.

In addition, the circuit modeling method of the printed circuit board according to an embodiment of the present invention forms a circuit model for each cell by forming a ladder and a resistor according to frequency so that the circuit characteristics at high frequency can be measured more accurately. do.

As described above, the present invention forms a circuit model for each cell by forming a ladder and a resistor according to the frequency in consideration of the skin effect to form characteristics of a printed circuit board having power planes and ground planes stacked on both sides of an insulator. The calculation time to calculate can be shortened.

In addition, the present invention forms a circuit model for each cell by forming a ladder and a resistor according to the frequency in consideration of the skin effect to form a circuit model for each part even if the port to be added to the part to know the circuit characteristics without recalculation process We can calculate the property of.

In addition, the present invention can more accurately measure the circuit characteristics at a high frequency by forming a ladder and a circuit model for each cell by forming a ladder and a resistor according to frequency.

Claims (6)

a) dividing a printed circuit board having a ground plane and a power plane stacked on both sides of an insulator in a matrix form at one tenth or less of a wavelength with respect to a frequency of interest; And b) n inductors having different inductances are connected in series according to the frequency of the cells between the nodes where the divided parts meet, and n + 1 resistors are connected in parallel across the n inductors. An external inductor and a first capacitor are connected in series between one side of a first resistor and a common terminal of the first inductor of the inductor and a ground, and between the other side of the first resistor, which is a common terminal of the n + 1 resistors, and the ground. And modeling the second capacitor as a series-connected circuit. The method of claim 1, And the n inductors have smaller inductance values from the center of the ground plane and the power plane to the edges of the n inductors. The method of claim 1, And the n + 1 resistors have a larger resistance value toward the edge from the center of the ground plane and the power plane. The method of claim 1, The step b) includes the step of setting a cell located at the edge of the printed circuit board of the cells as a half cell, and setting the remaining cells other than the half cell as a full cell, the circuit modeling of the printed circuit board Way. The method of claim 4, wherein Printed circuit, characterized in that the half cell resistance, inductor and external inductor is twice as large as the full cell resistance, inductor and external inductor, and the half cell capacitor is 1/2 of the full cell capacitor. Circuit modeling method of the board. The method of claim 1, The resistance of the printed circuit board is measured by VNA, and the skin effect range is calculated using the measured resistance to determine a resistance change constant according to metal roughness, a rate of increasing resistance, and a rate of increasing inductor. Circuit modeling method of printed circuit board.

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