Chain self-noise measurement circuit and method based on noise self-excitation

Abstract

This invention relates to the field of noise measurement technology, specifically disclosing a chain-type self-noise measurement circuit based on noise self-excitation. The circuit includes multiple preamplifiers, a power supply, and a measuring device. The preamplifiers are connected sequentially and each is connected to the power supply. The last preamplifier is connected to the measuring device. This invention also discloses a chain-type self-noise measurement method based on noise self-excitation. Compared to traditional measurement methods, this invention does not introduce high-magnification amplifiers, resulting in a simpler structure, easier operation, and avoidance of noise effects caused by complex circuits. By employing a chain-type measurement structure and selecting an appropriate number of amplification stages based on the noise level, the output noise overwhelms the background noise of the measuring device, thereby eliminating the influence of the measuring device's background noise.

Description

Technical Field

[0001] This invention relates to the field of noise measurement technology, and in particular to a chain-type self-noise measurement circuit and method based on noise self-excitation. Background Technology

[0002] In the field of precision signal link design, noise is a crucial parameter for the entire system. On the one hand, as a random signal, noise can easily cause adverse effects on electronic circuits, such as spikes, ripples, or oscillations, which can lead to system damage in severe cases. On the other hand, as a small analog signal, noise is so difficult for most standard measuring devices to measure accurately. As the weak signal receiver in a precision signal link, the preamplifier is easily affected by irregular external and internal radiation and interference. Its self-noise plays a decisive role in the high signal-to-noise ratio and high-fidelity performance of the entire system.

[0003] The impact of noise is particularly widespread. For example, in mobile communication technology applications, the presence of noise can cause signal distortion, a poor channel environment, and a high packet loss rate and bit error rate, which will prevent communication from being carried out correctly and effectively. In industrial high-precision instrument measurement applications, the measured signal can easily be overwhelmed by noise signals, and the presence of noise will seriously affect the measurement accuracy and resolution of the instrument. Furthermore, in the practical application of hydrophone arrays, the preamplifier, as the receiver of weak underwater acoustic signals, has a significant impact on underwater acoustic acquisition, real-time transmission, waveform reconstruction, and other aspects due to its noise characteristics.

[0004] Circuit noise limits system sensitivity, false trigger rate, resolution, and other performance indicators, and is difficult to eliminate. However, the nature of the noise can be analyzed based on noise measurement results, allowing for efforts to reduce its intensity or improve the circuit's immunity to prevent interference. Therefore, measuring self-noise in a circuit is crucial.

[0005] With the deepening development of noise research, noise measurement technology has also been significantly improved. Early noise measurement methods primarily relied on simulation testing to obtain noise levels in specific frequency bands of electronic devices. However, with continuous advancements in technology, researchers began utilizing circuit analysis principles to transform actual circuits into noise equivalent models for analysis and calculation. In recent years, the demand for high noise immunity in precision signal links has made noise an increasingly important indicator in engineering applications. Noise measurement has gradually evolved into integrating low-noise amplifiers and filters into high-power amplifiers with filtering capabilities, thereby enabling the acquisition of noise time-domain and frequency-domain measurement results. This has become the mainstream noise measurement method.

[0006] Existing noise measurement techniques are mainly divided into two categories: equivalent noise source analysis and peripheral circuit measurement. The former requires transforming the actual circuit into a noise equivalent model for analysis and calculation. It not only needs to consider voltage noise sources, current noise sources, and resistive thermal noise sources, but also the correlation between these noise sources. Therefore, the equivalent noise source analysis method is difficult to model and computationally complex when dealing with complex circuits. The latter requires the use of peripheral circuits such as high-power amplifiers to amplify the noise to be measured before measurement. However, this introduces new peripheral circuit noise, the value of which is difficult to estimate.

[0007] The self-noise of a real circuit is related to various factors, such as voltage noise, current noise, thermal noise from circuit resistors, power supply noise, electromagnetic interference noise, and ground loop noise. In recent years, researchers have achieved significant noise reduction results through continuous optimization of circuit power supplies and their routing. Therefore, when performing noise analysis, only the remaining noise sources in the circuit need to be considered.

[0008] In the paper "Noise Analysis and Improvement of Preamplifier Circuit for Underwater Acoustic Receiver," the existing circuit is transformed into a noise equivalent model based on noise principles. The equivalent noise source analysis method is then used to perform noise analysis and calculations on the preamplifier circuit of the underwater acoustic receiver. Common amplifier circuit noise models used in the paper include... Figure 1 As shown. Figure 1 The noise voltage density of the amplifier chip is V N The resistive thermal noise voltage density at the non-inverting and inverting terminals is V. N,R3 V N,R1 and V N,R2 Among them, resistive thermal noise exists. (k is the Boltzmann function, T is the thermodynamic temperature), current noise I N The noise voltage density generated at the input terminal is V. N,I According to the principle of noise superposition, the root sum of the squares of the noise voltage densities of each independent noise source is the total noise voltage density. The analytical calculation examples and noise equivalent model circuits used in this paper are as follows: Figure 2 and Figure 3 As shown.

[0009] In the paper "Calculation of Noise Spectrum Matrix and Analysis of Noise Performance of Integrated Operational Amplifier Circuit", considering the correlation between the equivalent input noise voltage source and current source of the preamplifier itself, it is proposed to use the noise spectrum matrix to obtain the voltage-current noise of the preamplifier circuit, so that the correlation of the noise source of the preamplifier is fully considered.

[0010] The methods described above all involve converting the actual circuit into a noise equivalent model for analysis and calculation. These methods are widely used in scientific research, while mainstream noise measurement primarily relies on peripheral circuit measurement. Because the noise amplitude is too low, directly connecting the output of the circuit under test to the measuring equipment results in difficulty obtaining accurate data waveforms or values ​​at the measuring equipment due to the equipment's inherent noise floor. Therefore, when measuring circuit noise, a high-powered amplifier is often added between the circuit under test and the measuring equipment. Generally, the noise floor of the high-powered amplifier should be at least three times lower than the output noise of the circuit under test.

[0011] Chinese Patent Publication No. CN207780123U discloses a low-frequency noise measurement device, which consists of a high-gain preamplifier and a low-gain post-filter connected in sequence. This device represents the basic structure of a common noise measurement peripheral circuit (i.e., the aforementioned high-gain amplifier). Taking this device as an example, when measuring noise, the noise of the circuit under test is amplified to a level higher than the noise floor of the measuring device and easily observed at the device end, thus allowing the noise of the circuit under test to be reflected in the measurement. A common noise measurement peripheral circuit is shown in Figure 4.

[0012] Chinese Patent Publication No. CN101945070B discloses a noise measurement method in the field of communication technology. The method includes: performing a first noise measurement based on frequency domain data obtained after FFT (Fast Fourier Transform); performing channel estimation using the result of the first noise measurement; and performing a second noise measurement based on the frequency domain data and the channel estimation result, with the measurement result used for subsequent processing. This method performs an additional noise measurement on top of existing noise measurement methods, improving the accuracy of the noise measurement results and ensuring superior performance under various channel conditions. The flowchart of this method is shown below. Figure 5 As shown.

[0013] The method proposed in the paper "Noise Analysis and Improvement of Preamplifier Circuit for Underwater Acoustic Receiver" requires evaluating the noise contribution of each part of the circuit and identifying the main noise types to analyze and calculate the circuit noise. This method is aimed at... Figure 2 For the simple circuit shown, the computational difficulty is moderate. However, when dealing with complex circuits, the difficulty and computational load increase significantly due to the large number of components, complex structure, and numerous noise sources.

[0014] The method proposed in the paper "Calculation of Noise Spectrum Matrix and Noise Performance Analysis of Integrated Operational Amplifier Circuit" only considers the correlation between the equivalent input voltage and current noise sources of the amplifier itself, which already increases the difficulty of noise analysis calculation. However, there is correlation between various noise sources in the circuit. It is conceivable that for a complex circuit, the computational complexity will increase exponentially. In addition, reading errors during the calculation process and neglected correlation effects (such as temperature) will also lead to increased error in the results.

[0015] The method proposed in patent CN207780123U requires that the noise floor of the high-magnification amplifier be lower than the output noise of the circuit under test when measuring noise using this method. Its drawbacks are as follows: First, there is no standardized selection criteria for high-magnification amplifiers, making it difficult to directly find devices with noise levels three times lower than those of the circuit under test; second, to ensure that the self-noise of the high-magnification amplifier is lower than that of the circuit under test, the self-noise of the high-magnification amplifier needs to be measured, and the measured self-noise of the high-magnification amplifier may not be accurate or reliable; third, the self-noise of the high-magnification amplifier can also become a noise source in the measurement process, and its self-noise can introduce errors into the measurement results.

[0016] The method proposed in patent CN101945070B requires computational processing for each module used in noise measurement, resulting in a complex structure and high requirements for each module. For example, the method involves an FFT module and two noise measurement modules. Before the first measurement, the FFT module must perform a frequency domain transformation on the noise, and each noise measurement module must calculate the noise variance. Furthermore, this method only measures channel noise in the field of communication technology, limiting its application.

[0017] In summary, existing noise measurement technologies suffer from drawbacks such as high computational complexity, complex structure, and low accuracy. Summary of the Invention

[0018] To address the problems of high computational complexity, complex structure, and low accuracy in existing noise measurement techniques, this invention provides a method that simplifies process calculations, minimizes the impact of objective factors such as equipment background noise, and accurately measures the equivalent input noise N of a preamplifier. i (f) A chain-type self-noise measurement circuit and method based on noise self-excitation to ensure accurate and effective noise measurement results at the equivalent input terminal of the module under test.

[0019] The technical solution adopted in this invention is:

[0020] A chain-type self-noise measurement circuit based on noise self-excitation includes multiple preamplifiers, a power supply, and a measuring device. The multiple preamplifiers are connected sequentially, each connected to the power supply, and the preamplifier at the end is connected to the measuring device. Figure 6 The diagram shows the forward propagation process of the effective value of the noise voltage.

[0021] Preferably, the multiple preamplifiers use the same model.

[0022] Preferably, the plurality of said preamplifiers are equidistantly distributed.

[0023] Preferably, the differential input terminals of the preamplifier at the front end are short-circuited to ground, the differential input terminals of the remaining preamplifiers are respectively connected to the differential output terminals of the preceding preamplifier, the differential positive output terminal of the preamplifier at the rear end is connected to the measuring device, and the differential negative output terminal is left floating.

[0024] A measurement method for a chain-type self-noise measurement circuit based on noise self-excitation includes the following steps:

[0025] A chain structure of multi-stage preamplifier circuits is constructed. The structure includes multiple preamplifier circuits, a power supply, and a measuring device. The multiple preamplifiers are connected in sequence, and each of the multiple preamplifiers is connected to the power supply. The preamplifier at the last end is connected to the measuring device.

[0026] The background noise N of the measuring equipment was measured. osc (f);

[0027] By shorting and grounding the input terminals of the first-stage preamplifier, the influence of environmental noise and electronic component noise can be avoided, thereby enabling accurate measurement of the preamplifier's equivalent input noise N. i (f);

[0028] By connecting the input and output terminals of adjacent preamplifiers sequentially according to the same polarity principle, multi-stage amplification of self-noise can be achieved. By appropriately selecting the number of amplification stages, the self-noise of the preamplifier can be amplified to a level that can completely submerge the background noise N of the measuring equipment. osc (f) is more than m times and is ignored. The value of m can be selected according to the actual range of the measuring equipment so that the input voltage of the measuring equipment is less than the range of the measuring equipment.

[0029] The derivation of each stage in the multi-stage amplifier circuit is performed, and the voltage gain of each stage of the individual amplifier circuit is measured.

[0030] Assume the voltage gain of the i-th stage is A. i The equivalent output noise voltage of this stage of the circuit is K. iThe equivalent input noise voltage of the operational amplifier in this stage is N. i (f), the effective value of the total noise voltage at the output terminal is N valid (f) Calculate the equivalent output noise voltage of the first stage, and so on, to obtain the equivalent noise voltages k2, k3, ..., k at the final output of the nth stage. n With N valid (f), where:

[0031] k1=A1×N1(f)(1)

[0032]

[0033]

[0034]

[0035]

[0036] Each stage uses the same type of amplifier, therefore the A of each stage is... i With N i (f) are all the same, let A(f) and N be taken as... i (f) Iteratively rearrange equations (1), (2), (3), and (4) to obtain N. valid (f) Regarding A(f), N i (f), N osc The expression for (f):

[0037]

[0038] The beneficial effects of this invention are:

[0039] 1. Compared with traditional measurement methods, it does not introduce a high-magnification amplifier, has a simple structure, is easy to operate, and avoids the noise influence caused by complex circuits;

[0040] 2. A chain-type measurement structure is adopted, and an appropriate number of amplification stages are selected according to the noise level so that the output noise drowns out the background noise of the measuring equipment, thereby eliminating the influence of the background noise of the measuring equipment. Attached Figure Description

[0041] Figure 1 This is a common amplifier circuit noise model used in the paper "Noise Analysis and Improvement of Preamplifier Circuit for Underwater Acoustic Receiver";

[0042] Figure 2 For the underwater acoustic receiver preamplifier circuit in the paper "Noise Analysis and Improvement of Underwater Acoustic Receiver Preamplifier Circuit"

[0043] Figure 3This is the noise equivalent model circuit of the preamplifier circuit in the paper "Noise Analysis and Improvement of Preamplifier Circuit for Underwater Acoustic Receiver";

[0044] Figure 4 This is a schematic diagram of a common peripheral circuit structure for noise measurement.

[0045] Figure 5 This is a flowchart of a noise measurement method;

[0046] Figure 6 A schematic diagram of the forward propagation of the effective value of the output noise voltage;

[0047] Figure 7 This is a schematic diagram of the connection of a three-stage preamplifier circuit. Detailed Implementation

[0048] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0049] Example

[0050] A chain-type self-noise measurement circuit based on noise self-excitation includes multiple preamplifiers, a power supply, and a measuring device. The multiple preamplifiers are connected in sequence and are respectively connected to the power supply. The preamplifier located at the last end is connected to the measuring device.

[0051] Specifically, multiple preamplifiers use the same model.

[0052] Specifically, the multiple preamplifiers are equidistantly distributed.

[0053] Specifically, the differential input terminals of the preamplifier at the front end are shorted to ground, the differential input terminals of the remaining preamplifiers are connected to the differential output terminals of the preceding preamplifiers respectively, the differential positive output terminal of the preamplifier at the rear end is connected to the measuring device, and the differential negative output terminal is left floating.

[0054] The measuring device can be an oscilloscope. Preamplifiers are connected by wires, and the preamplifiers are connected to the power supply by power lines. The preamplifier circuit is connected to the oscilloscope via an oscilloscope probe. Figure 7As shown, taking three preamplifiers (denoted as A1, A2, and A3 respectively) as an example, the essence of the three-stage preamplifier circuit structure is to cascade three single-stage preamplifiers into a three-stage preamplifier, thereby amplifying the self-noise of the single-stage preamplifier A1. Without introducing other noise, it achieves the purpose of accurately monitoring and analyzing weak noise. After processing by numerical calculation tools (such as MATLAB), the noise spectral density curve can be obtained. The differential input terminals Pi_1 and Ni_1 of preamplifier A1 are shorted to ground. Preamplifier A1 is connected to the power supply via a power line. The differential input terminals Pi_2 and Ni_2 of preamplifier A2 are connected to the differential output terminals Po_1 and No_1 of preamplifier A1, respectively. Preamplifier A2 is connected to the power supply via a power line. The differential input terminals Pi_3 and Ni_3 of preamplifier A3 are connected to the differential output terminals Po_2 and No_2 of preamplifier A2, respectively. Preamplifier A2 is connected to the power supply via a power line. The positive differential output terminal Po_3 of preamplifier A3 is connected to oscilloscope probe and oscilloscope channel 1. The negative differential output terminal No_3 of preamplifier A3 is left floating. All signal lines in the circuit are connected point-to-point according to the principle of the same polarity to reduce the trace distance. Twisting of differential lines is used to eliminate common-mode noise. Signal ground and power ground are connected at a single point. The power supply is a linear regulated power supply connected in a star configuration. The linear regulated power supply is configured in series, ensuring its output corresponds to the ±VCC DC voltage of the preamplifier circuit. The power supply line width for the circuit is at least 30 mils. The oscilloscope's sampling rate is determined according to the Nyquist sampling theorem, with DC coupling, standard sampling mode, 1MΩ channel load, and a 1:1 probe attenuation ratio. The oscilloscope probe loop is minimized, and the probe cable is kept as far away from radiation sources as possible to avoid picking up spatial radiated noise. During testing, the three-stage preamplifier circuit is placed in a shielded box or sealed with aluminum foil, as far away from radiation sources as possible.

[0055] The phenomenon of "self-oscillation" refers to the phenomenon where a circuit still outputs a voltage with a certain amplitude and frequency when there is no input signal. This invention cleverly utilizes the principle of noise "self-oscillation" to measure the self-noise of a preamplifier circuit. Figure 7 The action is described as follows:

[0056] 1. The differential input terminals Pi_1 and Ni_1 of preamplifier A1 are shorted to ground. The input noise of preamplifier A1 (i.e., the self-noise of preamplifier A1) is amplified by A1 to obtain the output noise of preamplifier A1. The output noise of preamplifier A1 is output through the differential output terminals Po_1 and No_1 of preamplifier A1.

[0057] 2. The output noise of preamplifier A1 and the self-noise of preamplifier A2 are superimposed in the form of "square root" to form the input noise of preamplifier A2. The input noise of preamplifier A2 is amplified by A2 to obtain the output noise of preamplifier A2. The output noise of preamplifier A2 is output through the differential output terminals Po_2 and No_2 of preamplifier A2.

[0058] 3. The output noise of preamplifier A2 and the self-noise of preamplifier A3 are superimposed in the form of "square root" to form the input noise of preamplifier A3. The input noise of preamplifier A3 is amplified by A3 to obtain the output noise of preamplifier A3.

[0059] 4. The output noise of preamplifier A3 is the result of the self-noise of preamplifier A1 after three stages of amplification.

[0060] 5. The noise at the output of preamplifier A3 is fed into an oscilloscope. After sampling, A / D (Analog to Digital) conversion, and microprocessor processing, the time-domain waveform of the noise at the output of preamplifier A3 is displayed on the oscilloscope screen.

[0061] A measurement method for a chain-type self-noise measurement circuit based on noise self-excitation includes the following steps:

[0062] A chain structure of multi-stage preamplifier circuits is constructed. The structure includes multiple preamplifier circuits, a power supply, and a measuring device. The multiple preamplifiers are connected in sequence, and each of the multiple preamplifiers is connected to the power supply. The preamplifier at the last end is connected to the measuring device.

[0063] The background noise N of the measuring equipment was measured. osc (f);

[0064] By shorting and grounding the input terminals of the first-stage preamplifier, the influence of environmental noise and electronic component noise can be avoided, thereby enabling accurate measurement of the preamplifier's equivalent input noise N. i (f);

[0065] By connecting the input and output terminals of adjacent preamplifiers sequentially according to the same polarity principle, multi-stage amplification of self-noise can be achieved. By appropriately selecting the number of amplification stages, the self-noise of the preamplifier can be amplified to a level that can completely submerge the background noise N of the measuring equipment. osc (f) is more than m times and is ignored. The value of m can be selected according to the actual range of the measuring equipment so that the input voltage of the measuring equipment is less than the range of the measuring equipment.

[0066] The derivation of each stage in the multi-stage amplifier circuit is performed, and the voltage gain of each stage of the individual amplifier circuit is measured.

[0067] Assume the voltage gain of the i-th stage is A. i The equivalent output noise voltage of this stage of the circuit is K. i The equivalent input noise voltage of the operational amplifier in this stage is N. i (f), the effective value of the total noise voltage at the output terminal is N valid (f) Calculate the equivalent output noise voltage of the first stage, and so on, to obtain the equivalent noise voltages k2, k3, ..., k at the final output of the nth stage. n With N valid (f), where:

[0068] k1=A1×N1(f)(1)

[0069]

[0070]

[0071]

[0072]

[0073] Each stage uses the same type of amplifier, therefore the A of each stage is... i With N i (f) are all the same, let A(f) and N be taken as... i (f) Iteratively rearrange equations (1), (2), (3), and (4) to obtain N. valid (f) Regarding A(f), N i (f), N osc The expression for (f):

[0074]

[0075] This invention requires testing in a vacuum or foil-sealed environment to reduce the impact of environmental noise and radiation interference on the measurement circuit.

[0076] This invention is theoretically applicable not only to Figure 7 The aforementioned working mode may also be applied to, but is not limited to, the following aspects:

[0077] 1. Generally, the present invention is not limited to a three-stage cascaded structure. Theoretically, it can be applied to an N-stage amplifier circuit to measure infinitesimal noise levels, depending on the noise level.

[0078] 2. Generally, the present invention is not limited to dual-input dual-output amplifier circuits in precision signal links, but can theoretically be applied to dual-input single-output, single-input single-output, and single-input dual-output amplifier circuits.

[0079] 3. Generally, the present invention is not limited to the dual-power supply amplifier circuit described in technical solution 4.2, but is theoretically applicable to any dual-power supply (-VCC-+VCC) or single-power supply (+VCC) amplifier circuit.

[0080] 4. Generally, the present invention is not limited to the measurement of self-noise of preamplifiers in precision signal links, but can also be applied to the measurement of any weak signal in precision signal links, and can also be used to measure the noise of any precision instrument.

[0081] 5. Generally, for weak signals with small amplitude and low frequency, the output terminal of such signals can be connected to the input terminal of the first-stage amplifier circuit described in this invention, thereby amplifying the weak signals. During data processing, only the amplifier gain needs to be considered to obtain the characteristics of the original input signal. Therefore, this invention can be used as a precision instrument to measure any weak signal.

[0082] Compared with the prior art, the present invention has the following advantages:

[0083] 1. Compared with the method proposed in the patent with publication number CN207780123U: This invention uses a chain measurement method to measure the self-noise of the preamplifier circuit. Structurally, it uses N preamplifiers of identical specifications cascaded together. On the basis of achieving noise measurement, it effectively avoids the influence of different models (such as connecting high-power amplifiers) and the background noise of the measuring equipment on the circuit under test, thus ensuring the accuracy of the measurement results.

[0084] 2. Compared to the method proposed in patent CN101945070B: This invention has a simpler structure, consisting mainly of N preamplifier circuits, and requires no special data processing for any of the preamplifier circuits. Furthermore, the entire process requires only one measurement, ensuring the speed of the measurement process.

[0085] 3. Compared with the methods proposed in the papers "Noise Analysis and Improvement of Preamplifier Circuit for Underwater Acoustic Receiver" and "Noise Spectrum Matrix Calculation and Noise Performance Analysis of Integrated Operational Amplifier Circuit", this invention can be applied to any simple or complex circuit form without converting the circuit into a noise equivalent model. The calculations used in the invention method are simpler than the equivalent noise source analysis method, avoiding the complexity of circuit modeling and analysis calculations.

[0086] 4. This invention does not have special requirements for measurement equipment and can theoretically be applied to standard measurement equipment such as true RMS meters, spectrum analyzers, and oscilloscopes, including but not limited to the above-mentioned equipment, thus ensuring flexibility in the selection of measurement equipment.

[0087] 5. The method of the present invention can not only measure the self-noise of a circuit, but also be used as a precision instrument. It can be used to measure any weak signal in any field, such as any noise source in a complex circuit or a noise source in a channel in the field of communication technology, thus ensuring the wide applicability of the measurement method.

[0088] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A chain self-noise measuring circuit based on noise self-excitation, characterized by, It includes multiple preamplifiers, a power supply, and a measuring device. The multiple preamplifiers are connected in sequence and are respectively connected to the power supply. The differential input terminals of the preamplifier at the front end are shorted to ground. The differential input terminals of the remaining preamplifiers are respectively connected to the differential output terminals of the previous preamplifier. The differential positive output terminal of the preamplifier at the rear end is connected to the measuring device, and the differential negative output terminal is left floating. The measurement method for this chain-type self-noise measurement circuit is as follows: Measuring the background noise of a measuring device ; Measuring the equivalent input noise of a preamplifier ; The derivation of each stage in the multi-stage amplifier circuit is performed, and the voltage gain of each stage of the individual amplifier circuit is measured. Assume the first The voltage gain of the stage is The equivalent output noise voltage of this stage of the circuit is The equivalent input noise voltage of the operational amplifier in this stage is The effective value of the total noise voltage at the output terminal is The equivalent output noise voltage of the first stage is calculated, and so on, to obtain the second, third, and... Until the last one The equivalent noise voltage at the stage and the final output terminal , , , and ,in: （1） （2） （3） （4） （5） Each stage uses the same model of amplifier, therefore each stage... and All are the same, take as and By iteratively rearranging equations (1), (2), (3), and (4), we obtain... about , , The expression: （6）。 2. The chain-type self-noise measurement circuit based on noise self-excitation according to claim 1, characterized in that, Multiple of the aforementioned preamplifiers use the same model.

3. The chain-type self-noise measurement circuit based on noise self-excitation according to claim 2, characterized in that, The preamplifiers are distributed at equal intervals.

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