Pdf prediction method based on impulse response pdn network voltage noise

Abstract

The present application provides a PDF prediction method based on impulse response PDN network voltage noise, which is used to solve the problem of excessive design of power distribution network caused by large error of result when predicting the voltage noise of the entire power distribution network according to the worst current of a single transistor and ignoring the probability of occurrence of the worst voltage noise of the power distribution network. The implementation steps are: generating an impulse response waveform of the time domain simulation of the power distribution network; generating a pulse vector of the impulse response waveform; calculating a response voltage vector of the input current of the power distribution network; calculating a probability vector corresponding to the response voltage vector; predicting the voltage noise and the probability density distribution of the power distribution network. The present application can efficiently and accurately predict the voltage noise and the probability density distribution of the power distribution network, and can provide a reference for analyzing the power integrity when designing the PDN network.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of electricity, and more particularly to the field of digital information transmission, and relates to a method for predicting the probability density function (PDF) of voltage noise in a power distribution network (PDN) based on impulse response. The present application can be used to predict the probability density distribution of voltage noise in a power distribution network in a high-speed circuit system, and accordingly, can provide a reference for analyzing the power integrity of a PDN network during design. BACKGROUND

[0002] A power distribution network is composed of power modules, capacitors on a printed circuit board (PCB), power and ground planes, and capacitors in a chip package. The main function of a power distribution network is to maintain a constant supply voltage between chip pads and to keep the supply voltage within a small tolerance range, usually within 5%, to meet the system requirements for power stability. As the clock frequency of chips continues to increase, the switching speed of transistors inside the load chip is getting faster and faster, resulting in an increasing demand for high-frequency transient current in the load. Therefore, it is necessary to design a power distribution network reasonably. Currently, the optimization design of a power distribution network is mainly based on target impedance, i.e., controlling the impedance of the power distribution network to be less than the target impedance. The target impedance is the ratio of the maximum noise voltage to the maximum transient current that the system can tolerate. For a good power distribution network, the size of voltage noise and its probability of occurrence are within the acceptable range of the power distribution network design under any circumstances, and the system meets the design requirements. The worst voltage noise is the maximum voltage noise that occurs in a power distribution network. If the probability of the occurrence of the worst voltage noise is extremely low, but it is used as a standard to design the power distribution network, then overdesign of the power distribution network will occur.

[0003] Xi'an University of Electronic Science and Technology discloses a worst power supply noise prediction method in its applied patent document "A precise prediction method for worst power supply noise of high-speed circuit system" (application number: 201710049054.0, authorized publication number: CN 106886636 B). The implementation steps of the method are: performing frequency domain simulation on the power distribution network to obtain the frequency domain self-impedance curve of the power distribution network output port; determining the anti-resonance frequency value corresponding to the maximum peak value in the power distribution network frequency domain self-impedance curve, and using the anti-resonance frequency value to modulate the periodic rectangular wave with a duty cycle of 50% to obtain the input code type causing the worst power supply noise; simulating the rising current and falling current of the power distribution network output port; predicting the worst current of the power distribution network output port; calculating the time domain impedance of the power distribution network; and calculating the worst power supply noise of the high-speed circuit system. The method improves the prediction accuracy to a certain extent under the premise of ensuring efficiency and can be applied to the analysis of signal integrity in high-speed circuit systems. However, the patent still has the following shortcomings: the method only randomly selects one transistor and models the selected transistor, approximates the switching current of the transistor to a triangular wave current, obtains the predicted worst current of the transistor, and uses the worst current to predict the worst voltage noise of the power distribution network. However, in engineering practice, the load chip contains thousands of transistors, and predicting the switching current of only one transistor of the load chip and using it to further predict the worst voltage noise of the entire power distribution network will result in a large error.

[0004] Sandle, Steven Picotest proposes a PDN network worst power supply noise prediction method in the published paper "Target Impedance Limitations and Rogue Wave Assessments on PDN Performance" (DesignCon Conference 2015 Steve@Picotest.com). The implementation steps of the method are: performing frequency domain simulation on the power distribution network to obtain the impedance curve of the power distribution network; constructing a load circuit composed of a series of current sources, which generate square wave current signals containing each anti-resonance frequency, while allowing the time delay of each current source to be adjusted; using the optimizer in the software ADS to optimize the delay of the current source of the circuit to find the worst predicted power supply noise. Using this method can predict the size of the worst voltage noise. However, this method still has the following shortcomings: the method only predicts the worst voltage noise, and if the probability of the occurrence of the worst voltage noise is extremely low, it may lead to overdesign of the power distribution network, resulting in waste of design time and design cost. SUMMARY

[0005] The present application aims at the deficiency of the prior art, and provides a PDF prediction method based on impulse response PDN network voltage noise, which is used to solve the problem of large error and overdesign of power distribution network caused by predicting the worst voltage noise of the entire power distribution network by using a single transistor.

[0006] The idea for realizing the present application is to use an ideal impulse current source as the load circuit of the power distribution network, to perform time-domain simulation on the entire power distribution network of the high-speed circuit system, and to obtain the impulse response waveform of the output port of the power distribution network. The present application uses the obtained impulse response of the entire power distribution network of the high-speed circuit system to predict the response voltage value and its occurrence probability of each bit of the input current source of the power distribution network when the code type is "1" and "0". In this process, the impulse response of the entire power distribution network is determined by the switching current of multiple transistors, rather than the switching current of a single transistor, thereby solving the problem of large error in the prediction result caused by predicting the worst voltage noise of the entire PDN network according to the switching current of a single transistor. The present application uses the obtained impulse response of the power distribution network to predict the response voltage value and its occurrence probability of the power distribution network, and analyzes based on this, thereby avoiding the problem of overdesign of the power distribution network.

[0007] The technical scheme adopted by the present application comprises the following steps:

[0008] Step 1: generating the impulse response waveform of the time-domain simulation of the power distribution network:

[0009] The time-domain simulator is used to control the time-domain simulation of the power distribution network, and the response voltage value of the impulse current at the output port of the power distribution network is obtained. The response voltage values at all sampling time points are plotted in time sequence to form the impulse response waveform.

[0010] Step 2: generating the impulse vector of the impulse response waveform:

[0011] The voltage value at the last sampling time point of the impulse response waveform is taken as the stable voltage value of the impulse response waveform. The voltage value at each sampling time point of the impulse response waveform is subtracted from the stable voltage value of the impulse response waveform to obtain the impulse vector of the impulse response waveform.

[0012] Step 3: calculating the response voltage vector of the input current of the power distribution network:

[0013] Step 3.1: controlling the current code type input to the power distribution network by using the voltage-controlled current source and the time-domain pseudo-random bit sequence voltage source;

[0014] Step 3.2: calculating the corresponding response voltage vector of the power distribution network when each bit of the binary sequence is "1" or "0";

[0015] Step 4, calculating the probability vector corresponding to the response voltage vector of the power distribution network when each bit symbol of the binary sequence is "1" or "0";

[0016] Step 5, predicting the voltage noise and the probability density distribution of the power distribution network:

[0017] Step 5.1, composing the response voltage probability density matrix ε of the power distribution network with the response voltage vector and the corresponding probability vector of the power distribution network, arranging all voltage values in the first row of the response voltage probability density matrix ε in the order of voltage from small to large to obtain the voltage noise vector V noise of the power distribution network;

[0018] Step 5.2, calculating the voltage noise vector V noise of the power distribution network and the corresponding probability density distribution vector according to the following formula:

[0019] P noise (q) = (∑ε(2,x)) / s, when ε(1,x) = V noise (q)

[0020] wherein P noise (q) represents the probability value of the qth column in the probability density distribution vector of the voltage noise of the power distribution network, q represents the column serial number of the voltage noise vector V noise of the power distribution network, q = 1, 2, 3,..., L, and L is the length of the voltage noise vector V noise ; ε(2,x) represents the probability value of the 2nd row and the xth column of the response voltage probability density matrix, x represents the column serial number of the response voltage probability density matrix, 1 ≤ x ≤ R, and R represents the column number of the response voltage probability density matrix; s represents the sampling point number of each symbol; ε(1,x) represents the voltage value of the 1st row and the xth column of the response voltage probability density matrix; V noise (q) represents the voltage value of the qth column of the voltage noise vector V noise of the power distribution network.

[0021] Compared with the prior art, the present application has the following advantages:

[0022] Firstly, the present application uses the impulse response of the entire power distribution network of the high-speed circuit system to predict the voltage noise thereof, and uses the impulse response of the entire network as the basis for predicting the voltage noise, so as to overcome the defect in the prior art that the voltage noise of the entire power distribution network is predicted according to the worst current of a single transistor, which leads to a large error in the prediction result, and thus the present application improves the accuracy of predicting the voltage noise of the entire power distribution network.

[0023] Secondly, the present application uses the impulse response of the whole power distribution network of high-speed circuit system as the basis to predict the voltage noise probability density distribution of the power distribution network, overcomes the problem of over-design of the power distribution network caused by predicting only the worst voltage noise of the power distribution network and ignoring its occurrence probability in the prior art, so that the voltage noise size and its occurrence probability obtained by the present application can be used to more accurately judge whether the power distribution network needs further optimization design when designing the power distribution network, avoid over-design of the power distribution network, thereby shortening the design time and saving the design cost. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 is the implementation flowchart of the present application;

[0025] Figure 2 is the schematic diagram of the pulse current output by the pulse current source of the present application;

[0026] Figure 3 is the simulation diagram of the present application. DETAILED DESCRIPTION

[0027] The present application will be further described in detail below in combination with the drawings and examples.

[0028] Referring to Figure 1 and examples, the specific steps of the implementation of the present application will be further described in detail.

[0029] Step 1, generate the impulse response waveform of the time domain simulation of the power distribution network.

[0030] The time domain simulator controls the power distribution network to perform time domain simulation, and obtains the response voltage value of the pulse current at the output port of the power distribution network. The response voltage values at all sampling time points are plotted in time sequence to form the impulse response waveform.

[0031] The time-domain simulation of the power distribution network controlled by the time-domain simulator refers to setting the direct-current power voltage of the power distribution network to 0V, connecting a pulse current source in series with an output port of the power distribution network as a load circuit of the power distribution network. One end of the pulse current source is connected to the output port of the power distribution network, and the other end is grounded, so that the pulse current source forms a loop with the power distribution network. The pulse current output by the pulse current source flows through the power distribution network and obtains the load voltage of the load circuit at the output port of the power distribution network. The power distribution network is controlled by the time-domain simulator to perform time-domain simulation in the nanosecond time range of [0, 10000]. The time interval of the time-domain simulation is 0.02ns. After the time-domain simulation is completed, the response voltage value of the pulse current at every 0.02ns time interval from the 0th second to the 10000th second is obtained at the output port of the power distribution network. The response voltage values of all sampling time points are plotted in time sequence to form a pulse response waveform.

[0032] The rise time of the pulse current source used in the simulation of the application is 0.4ns, the fall time is 0.4ns, the pulse width is 0.6ns, and the pulse period is 10000ns.

[0033] The following will be described in detail with reference to the accompanying drawings. Figure 2 The pulse current output by the pulse current source is further described in detail.

[0034] Figure 2 In the figure, the horizontal axis t represents the time of the pulse current output by the pulse current source, and the unit is second. The vertical axis I represents the current value of the pulse current output by the pulse current source, and the unit is ampere. Figure 2 In the figure, Rise represents the rise time of the pulse current output by the pulse current source, Fall represents the fall time of the pulse current output by the pulse current source, and Width represents the pulse width of the pulse current output by the pulse current source.

[0035] Step 2, generating the pulse vector of the pulse response waveform.

[0036] The voltage value of the last sampling time point of the pulse response waveform is taken as the steady voltage value of the pulse response waveform. The voltage value of each sampling time point of the pulse response waveform is subtracted by the steady voltage value of the pulse response waveform to obtain the pulse vector of the pulse response waveform.

[0037] Step 3, calculating the response voltage vector of the input current of the power distribution network.

[0038] Step 3.1, the current pattern of the input power distribution network is controlled by the voltage-controlled current source and the time-domain pseudo-random bit sequence voltage source. That is, the voltage-controlled current source and the time-domain pseudo-random bit sequence voltage source are connected in series as a load current source, the load current source is connected to the power distribution network in the same way as step 1, the output voltage of the time-domain pseudo-random bit sequence voltage source is used to control the output current of the voltage-controlled current source, and the output current of the voltage-controlled current source controls the current pattern of the input power distribution network.

[0039] The time-domain pseudo-random bit sequence voltage source used in the embodiment of the present application has a low level of 0V and a high level of 1V, a data bit rate of 1GHz, a data period of 1ns, a rising edge time of 0.4ns, and a falling edge time of 0.4ns. The time-domain pseudo-random bit sequence voltage source outputs a voltage corresponding to each data period according to the input binary sequence. When the input binary symbol is "0", the low level is output; when the input binary symbol is "1", the high level is output, and the unit time interval UI of the binary symbol is 1ns.

[0040] The output voltage of the time-domain pseudo-random bit sequence voltage source is used to control the output current of the voltage-controlled current source. The transfer conductance of the voltage-controlled current source used in the embodiment of the present application is 1S, and the output current of the voltage-controlled current source is obtained by multiplying the transfer conductance and the output voltage of the time-domain pseudo-random bit sequence voltage source, which controls the current pattern of the input power distribution network.

[0041] Step 3.2, the response voltage vector of the power distribution network corresponding to each binary symbol being "1" or "0" is calculated. Since the end time of the time-domain simulation in the embodiment of the present application is 10000ns, the data period is 1ns, and the sampling interval is 0.02ns, the pulse vector of the impulse response waveform corresponds to a 10000-bit binary sequence, and each symbol of the binary sequence has 50 sampling points.

[0042] Since the probability of each binary symbol being "1" or "0" in the binary sequence input to the time-domain pseudo-random bit sequence voltage source is 0.5, the response voltage vector of the power distribution network corresponding to each binary symbol being "1" is calculated according to the following formula:

[0043] V1(k)=[V1(k-1)+V pulse (i),V0(k-1)+V pulse (i)]

[0044] wherein V1(k) represents the response voltage vector of the power distribution network when the kth bit of the binary sequence is "1", k represents the serial number of each bit in the binary sequence, k = 1, 2, …, N, N is the length of the binary sequence corresponding to the impulse vector of the impulse response waveform; V1(k-1) represents the response voltage vector when the k-1th bit of the binary sequence is "1", V0(k-1) represents the response voltage vector when the k-1th bit of the binary sequence is "0", when k = 1, V1(k-1) = 0, V0(k-1) = 0; V pulse (i) represents the value of the i th element in the impulse vector V pulse , i and k have the same value.

[0045] When each bit of the binary sequence is "0", the response voltage vector of the power distribution network corresponding to V1(k-1) and V0(k-1) is formed.

[0046] Step 4, calculate the probability vector corresponding to the response voltage vector of the power distribution network when each bit of the binary sequence is "1" or "0".

[0047] According to the following formula, the probability vector corresponding to the response voltage vector of the power distribution network when each bit of the binary sequence is "1" is calculated:

[0048] p1(m) = [p1(m-1)*0.5, p0(m-1)*0.5]

[0049] wherein p1(m) represents the probability vector corresponding to the response voltage vector of the power distribution network when the mth bit of the binary sequence is "1", m and k have the same value; p1(m-1) represents the probability vector corresponding to the response voltage vector when the m-1th bit of the binary sequence is "1", p0(m-1) represents the probability vector corresponding to the response voltage vector when the m-1th bit of the binary sequence is "0", when m = 1, p1(m-1) = 0.5, p0(m-1) = 0.5.

[0050] When each bit of the binary sequence is "0", the probability vector p0(m) corresponding to the response voltage vector of the power distribution network is the same as p1(m).

[0051] Step 5, predict the voltage noise and probability density distribution of the power distribution network.

[0052] Step 5.1, form the response voltage probability density matrix ε of the power distribution network by combining the response voltage vector of the power distribution network and the probability vector corresponding thereto, and arrange all voltage values in the first row of the response voltage probability density matrix ε in the order of voltage from small to large to obtain the voltage noise vector V noise of the power distribution network.

[0053] The response voltage vector of the power distribution network and its corresponding probability vector are combined into a response voltage probability density matrix of the power distribution network according to the following formula:

[0054]

[0055] wherein ε represents the response voltage probability density matrix of the power distribution network, Vr1 represents the response voltage vector of the power distribution network when the last bit of the binary sequence is "1", Vr0 represents the response voltage vector of the power distribution network when the last bit of the binary sequence is "0", pr1 represents the probability vector corresponding to the response voltage vector of the power distribution network when the last bit of the binary sequence is "1", and pr0 represents the probability vector corresponding to the response voltage vector of the power distribution network when the last bit of the binary sequence is "0".

[0056] All voltage values in the first row of the response voltage probability density matrix ε are arranged in ascending order of voltage to obtain a voltage noise vector V noise of the power distribution network.

[0057] Step 5.2, the voltage noise vector V noise of the power distribution network is calculated according to the following formula:

[0058] P noise (q) = (∑ε(2,x)) / s, when ε(1,x) = V noise (q)

[0059] wherein P noise (q) represents the probability value of the qth column in the probability density distribution vector of the voltage noise of the power distribution network, q represents the column number of the voltage noise vector V noise of the power distribution network, q = 1, 2, 3,..., L, and L is the length of the voltage noise vector V noise of the power distribution network; ε(2,x) represents the probability value of the 2nd row and the xth column of the response voltage probability density matrix, x represents the column number of the response voltage probability density matrix, 1 ≤ x ≤ R, and R represents the column number of the response voltage probability density matrix; s represents the number of sampling points of each symbol; ε(1,x) represents the voltage value of the 1st row and the xth column of the response voltage probability density matrix; and V noise (q) represents the voltage value of the qth column of the voltage noise vector V noise of the power distribution network.

[0060] The effect of the present application is further illustrated below in combination with a simulation experiment:

[0061] 1. Conditions of the simulation experiment:

[0062] The hardware platform of the simulation experiment of the application is: the processor is Intel(R) Core(TM) i7-11700KF, the main frequency is 3.6 GHz, and the memory is 32 GB.

[0063] The software platform of the simulation experiment of the application is: Windows 10 operating system, Matlab 2021b software and ADS 2022 software.

[0064] 2. Simulation content and result analysis of simulation experiment:

[0065] The simulation experiment of the application is to build a power distribution network as shown in Figure 3 (a) in the software ADS 2022, Figure 3 (a) VDC represents a direct current voltage source with a voltage of 0V in the power distribution network, V represents the unit of voltage, L1 and L2 represent inductances with inductance values of 1nH and 130pH respectively, nH and pH represent the units of inductance nanhen and pihen respectively, R1, R2 and R3 represent resistances with resistance values of 2mOhm, 6mOhm and 0.01mOhm respectively, mOhm represents the unit of resistance milliohm, C1 and C2 represent capacitors with capacitance values of 0.8uF and 0.1uF respectively, uF represents the unit of capacitance microfarad, GND represents ground, and Uo is the output port of the power distribution network.

[0066] According to step 1 of the application, a pulse current source is used to add a pulse current of 0-1 ampere for 10000 nanoseconds to the power distribution network, and the voltage at the output port of the power distribution network is sampled at a time interval of 0.02 nanoseconds and a frequency of 50 gigahertz, so as to obtain the pulse response waveform at the output port of the power distribution network.

[0067] According to step 2 of the application, the pulse vector is obtained using the pulse response waveform of the power distribution network in step 1 of the application.

[0068] According to steps 3.2, 4 and 5 of the application, the voltage noise and probability density distribution of the power distribution network as shown in Figure 3 (a) are calculated.

[0069] According to step 3.1 of the application, the response voltage value of 1000000 binary sequences is obtained by simulating the power distribution network as shown in Figure 3 (a), the response voltage value obtained is rounded to 4 decimal places to obtain the response voltage value with an accuracy of 0.1mV, and the response voltage value of 1000000 binary sequences is statistically obtained to obtain the voltage noise and probability density distribution of the power distribution network.

[0070] The voltage noise and its probability density distribution obtained from the binary sequence response voltage values of the power distribution network are compared with the voltage noise and its probability density distribution of the power distribution network calculated according to the pulse vector of the power distribution network, and the results are shown in Figure 3 Fig. 2(b). Figure 3 In Fig. 2(b), the horizontal axis represents the voltage value of the voltage noise of the power distribution network in volts, and the vertical axis represents the probability corresponding to each voltage noise value. Figure 3 In Fig. 2(b), the solid line represents the voltage noise and its probability density distribution curve obtained from the binary sequence response voltage values of the power distribution network, and the dashed line represents the voltage noise and its probability density distribution curve of the power distribution network calculated according to the pulse vector of the power distribution network. From Figure 3 As can be seen from Fig. 2(b), the two curves basically coincide, indicating that the voltage noise and its probability density distribution of the power distribution network calculated by the present application are consistent with the actual simulation results.

Claims

1. A method for predicting a PDF based on impulse response PDN network voltage noise, characterized by, The method comprises the following steps: Step 1, generating the impulse response waveform of the time domain simulation of the power distribution network: The time domain simulator controls the power distribution network to perform time domain simulation, and the response voltage value of the impulse current is obtained at the output port of the power distribution network. The response voltage values at all sampling time points are plotted in time sequence to form the impulse response waveform; Step 2, generating the impulse vector of the impulse response waveform: The voltage value at the last sampling time of the impulse response waveform is taken as the stable voltage value of the impulse response waveform. The voltage value at each sampling time of the impulse response waveform is subtracted from the stable voltage value of the impulse response waveform to obtain the impulse vector of the impulse response waveform; Step 3, calculating the response voltage vector of the input current of the power distribution network: Step 3.1, controlling the current code type of the input power distribution network through the voltage-controlled current source and the time-domain pseudo-random bit sequence voltage source; Step 3.2, calculating the response voltage vector of the power distribution network when each bit of the binary sequence is "1" or "0"; Step 4, calculating the probability vector corresponding to the response voltage vector of the power distribution network when each bit of the binary sequence is "1" or "0"; Step 5, predicting the voltage noise and the probability density distribution of the power distribution network: Step 5.1, compose the response voltage probability density matrix ε of the power distribution network with the response voltage vectors of the power distribution network and their corresponding probability vectors, arrange all the voltage values in the first row of the response voltage probability density matrix ε in ascending order of voltage to obtain the voltage noise vector V of the power distribution network noise ; Step 5.2, calculate the power distribution network voltage noise vector V noise The corresponding probability density distribution vector: P noise (q) = (∑ε(2, x)) / s, when ε(1, x) = V noise (q) wherein P noise (q) represents the probability value of the qth column of the probability density distribution vector of the voltage noise of the power distribution network, q represents the column number of the voltage noise vector V noise of the power distribution network, q = 1, 2, 3,..., L, L is the length of the voltage noise vector V noise , ε(2, x) represents the probability value of the 2nd row and xth column of the response voltage probability density matrix, x represents the column number of the response voltage probability density matrix, 1 ≤ x ≤ R, R represents the column number of the response voltage probability density matrix, s represents the sampling point number of each symbol, ε(1, x) represents the voltage value of the 1st row and xth column of the response voltage probability density matrix, V noise (q) represents the voltage value of the qth column of the voltage noise vector V noise of the power distribution network.

2. The method of claim 1, wherein the PDF prediction is based on impulse response PDN network voltage noise. In step 1, the time domain simulator controls the power distribution network to perform time domain simulation, which means that the DC power voltage of the power distribution network is set to 0V, and a pulse current source is connected in series at the output port of the power distribution network as a load circuit. One end of the pulse current source is connected to the output port of the power distribution network, and the other end is grounded, so that the pulse current source forms a loop with the power distribution network. The load voltage of the load circuit is obtained at the output port of the power distribution network after the pulse current output by the pulse current source flows through the power distribution network.

3. The method of claim 1, wherein the method is based on impulse response PDN network voltage noise. In step 3.1, the current code type of the input power distribution network is controlled by the voltage-controlled current source and the time-domain pseudo-random bit sequence voltage source, which means that the voltage-controlled current source and the time-domain pseudo-random bit sequence voltage source are connected in series as a load current source. The same connection method as in step 1 is used to replace the pulse current source connected to the power distribution network with the load current source. The output voltage of the time-domain pseudo-random bit sequence voltage source is used to control the output current of the voltage-controlled current source, and the output current of the voltage-controlled current source controls the current code type of the input power distribution network.

4. The method of claim 1, wherein the method is based on impulse response PDN network voltage noise. In step 3.2, the response voltage vector of the power distribution network corresponding to each bit of the binary sequence being "1" or "0" is calculated as follows: When each bit of the binary sequence is "1", the response voltage vector of the power distribution network corresponding to each bit of the binary sequence is calculated as follows: V1(k) = [V1(k - 1) + V pulse (i), V0(k - 1) + V pulse (i)] wherein V1(k) represents the response voltage vector of the power distribution network when the kth bit of the binary sequence is "1", k represents the serial number of each symbol in the binary sequence, k = 1, 2, …, N, N is the length of the binary sequence corresponding to the pulse vector of the pulse response waveform; V1(k-1) represents the response voltage vector when the k-1th bit of the binary sequence is "1", V0(k-1) represents the response voltage vector when the k-1th bit of the binary sequence is "0", when k = 1, V1(k-1) = 0, V0(k-1) = 0; V pulse (i) represents the value of the i-th element in the pulse vector V pulse , i has the same value as k. When each bit of the binary sequence is "0", V1(k-1) and V0(k-1) form the response voltage vector of the power distribution network.

5. The method of claim 4, wherein the impulse response based PDN voltage noise is a function of the PDF prediction. In step 4, the probability vector corresponding to the response voltage vector of the power distribution network when each bit of the binary sequence is "1" or "0" is obtained as follows: p1(m) = [p1(m-1)*0.5, p0(m-1)*0.5] wherein p1(m) represents the probability vector corresponding to the response voltage vector of the power distribution network when the mth bit of the binary sequence is "1", m and k have the same value; p1(m-1) represents the probability vector corresponding to the response voltage vector when the (m-1)th bit of the binary sequence is "1", p0(m-1) represents the probability vector corresponding to the response voltage vector when the (m-1)th bit of the binary sequence is "0", when m = 1, p1(m-1) = 0.5, p0(m-1) = 0.5; when each bit of the binary sequence is "0", the probability vector p0(m) corresponding to the response voltage vector of the power distribution network is the same as p1(m).

6. The method of claim 1, wherein the method is based on impulse response PDN network voltage noise. The response voltage probability density matrix ε described in step 5.1 is as follows: wherein ε represents the response voltage probability density matrix of the power distribution network, Vr1 represents the response voltage vector of the power distribution network when the last bit of the binary sequence is "1", Vr0 represents the response voltage vector of the power distribution network when the last bit of the binary sequence is "0", pr1 represents the probability vector corresponding to the response voltage vector of the power distribution network when the last bit of the binary sequence is "1", and pr0 represents the probability vector corresponding to the response voltage vector of the power distribution network when the last bit of the binary sequence is "0".

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