CN111900938B - Nonlinear analysis method applied to multistage operational amplifier - Google Patents
Nonlinear analysis method applied to multistage operational amplifier Download PDFInfo
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- CN111900938B CN111900938B CN202010572708.XA CN202010572708A CN111900938B CN 111900938 B CN111900938 B CN 111900938B CN 202010572708 A CN202010572708 A CN 202010572708A CN 111900938 B CN111900938 B CN 111900938B
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F3/00—Amplifiers with only discharge tubes or only semiconductor devices as amplifying elements
- H03F3/42—Amplifiers with two or more amplifying elements having their dc paths in series with the load, the control electrode of each element being excited by at least part of the input signal, e.g. so-called totem-pole amplifiers
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Abstract
The invention discloses a nonlinear analysis method applied to a multistage operational amplifier, which comprises the following steps: first, the distortion term coefficients of each stage of the operational amplifier are calculated or simulated, and the distortion term coefficients mainly comprise transconductance nonlinear term coefficients and output conductance nonlinear term coefficients. Then, the amplitude-frequency relation of the input and the output of each stage of the operational amplifier in the closed loop state is obtained through simulation. Next, a closed loop output impedance at the third order intermodulation quantity (IM 3) frequency is calculated by dividing the open loop output impedance by the loop gain. Finally, the output of each stage of the operational amplifier and the total output third-order intermodulation quantity (IM 3) are calculated, so that the influence of the output third-order intermodulation quantity (IM 3) of each stage of the operational amplifier on the total output third-order intermodulation quantity (IM 3) is judged. The method is used for carrying out nonlinear analysis on the three-stage operational amplifier, and compared with a simulation result, the method is found to be simple and effective, and has high analysis result precision and wide engineering application value.
Description
Technical Field
The invention relates to a nonlinear analysis method applied to a multistage operational amplifier, and belongs to the technical field of analog operational amplifier design.
Background
With the development of CMOS process technology, the reduction in transistor size provides higher integration and performance for digital circuits. However, the reduction in transistor size has plagued analog op amp designs with low supply voltages. To ensure the signal-to-noise ratio (SNR) of the op-amp, the signal swing should be as large as possible, thus taking up a significant portion of the supply voltage. The voltage left to bias the circuit becomes smaller and it is more challenging to design an operational amplifier with high linearity. Furthermore, integrated radio systems such as WLAN and bluetooth require high linearity in a considerable bandwidth. Therefore, in a low supply voltage and high bandwidth multi-stage op amp design, it is critical to analyze and optimize the linearity of the op amp.
Disclosure of Invention
Technical problems: in order to overcome the defects in the prior art, the invention provides the nonlinear analysis method applied to the multistage operational amplifier, which is simple and effective compared with the traditional nonlinear analysis method of the operational amplifier, has high analysis result precision and wide engineering application value.
The technical scheme is as follows: in order to achieve the above purpose, the invention adopts the following technical scheme: a nonlinear analysis method applied to a multistage operational amplifier, comprising the steps of:
1) Calculating or simulating to obtain distortion term coefficients of each stage of the multistage operational amplifier in an open loop state;
2) Simulating to obtain the amplitude-frequency relation of the input and the output of each stage of the multistage operational amplifier in a closed loop state;
3) Calculating a closed loop output impedance at the third order intermodulation product frequency by dividing the open loop output impedance by the loop gain;
4) And calculating to obtain the output of each stage of the multi-stage operational amplifier and the total output third-order intermodulation quantity, so as to judge the influence of the output third-order intermodulation quantity of each stage of the multi-stage operational amplifier on the total output third-order intermodulation quantity.
In step 1), the transconductance nonlinear term coefficient and the output conductance nonlinear term coefficient of the ith stage of operational amplifier in the open loop state are obtained through calculation or simulation respectively.
Further, the step 4) specifically comprises:
first, the ith operational amplifier inputs two amplitudes A 1_i And A 2_i And the frequencies are omega respectively 1 And omega 2 The frequencies of the two third-order intermodulation products in the output current of the ith operational amplifier are respectively 2 omega 1 -ω 2 And 2ω 2 -ω 1 The method comprises the steps of carrying out a first treatment on the surface of the The injection current of the ith operational amplifier is the sum of nonlinear current caused by transconductance of the ith operational amplifier and nonlinear current caused by conductance, the injection current of the ith operational amplifier is multiplied by the closed loop output impedance of the ith operational amplifier to obtain the third-order intermodulation amount voltage injected by the ith operational amplifier, then the third-order intermodulation amount voltage injected by the ith operational amplifier is multiplied by an open loop transfer function from the output end of the ith operational amplifier to the top-layer output end of the multistage operational amplifier to obtain the third-order intermodulation amount of the output end of the ith operational amplifier, and finally the third-order intermodulation amount of each stage operational amplifier output end is accumulated to obtain the total output third-order intermodulation amount, so that the influence of the third-order intermodulation amount of each stage output of the multistage operational amplifier on the total output third-order intermodulation amount is judged.
The beneficial effects are that: the nonlinear analysis is carried out on the three-stage operational amplifier by adopting the method, and the comparison with the simulation result shows that the difference between the calculated value and the simulation value of the third-order intermodulation quantity (IM 3) output by the operational amplifier is mostly about 1dBm, and the maximum difference is not more than 2dBm. In addition, the nonlinear analysis method provided by the invention can find out which stage is dominant in the operational amplifier, and provides a simpler and more effective method for optimizing the linearity of the operational amplifier. Therefore, the nonlinear analysis method applied to the multistage operational amplifier provided by the invention has high analysis result precision and wide engineering application value.
Drawings
FIG. 1a is a single-ended equivalent circuit of a three-stage op amp loop;
FIG. 1b is a non-linear model of a single stage amplification circuit;
fig. 2 is a graph comparing the results of calculated and simulated values of the total output third order intermodulation quantity (IM 3) for a single circuit stage in a three-stage operational amplifier.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
The invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, a single ended equivalent circuit of a three stage op amp loop with no internal feedback is presented. The ith stage OTA single stage circuits are modeled as a transconductance (g mi ) Impedance Z oi And (3) loading, wherein the loading comprises an output resistor and a capacitor.
The nonlinear analysis method provided by the invention is modeled by taking each stage of the operational amplifier as a unit. Considering only two distortion terms, the first is the i-th stage operational amplifier transconductance nonlinear term g mNL3_i The second ith stage operational amplifier output conductance g dsNL3_i . The step of obtaining the output third order intermodulation amount (IM 3) is as follows.
Step 1: first, some parameters of each stage of the operational amplifier need to be simulated or calculated. The nonlinear coefficient g of the ith stage operational amplifier of the multi-stage operational amplifier in the open loop state is obtained through simulation mNL3_i And g dsNL3_i 。
Step 2: and simulating to obtain the amplitude-frequency relation of the input and the output of each stage of the operational amplifier in a closed loop state.
Step 3: by passing open loop output impedance Z oOL_i Dividing by loop gain to calculate third order intermodulation quantity (IM 3) frequency f IM3 Closed loop output impedance Z at oCL_i 。
And 4, calculating the output intermodulation quantity generated by each stage. To find intermodulation injection quantity, the ith stage op amp needs to input two inputs with amplitudes A 1_i And A 2_i And the frequencies are omega respectively 1 And omega 2 Two third-order intermodulation quantity (IM 3) frequencies in the ith stage output current are respectively located at 2ω 1 -ω 2 And 2ω 2 -ω 1 The magnitude of which depends on the signal amplitude of the input and output.
The ith stage is:
wherein, the liquid crystal display device comprises a liquid crystal display device,and->Respectively, nonlinear current caused by transconductance and nonlinear current caused by conductance of the ith stage of operational amplifier, G i (ω k ) Is at frequency omega k The i-th gain at, k=1, 2, < G i (ω 1 )、∠G i (ω 2 ) At frequency omega, respectively 1 At the ith gain at frequency omega 2 The i-th gain at, |·| represents taking absolute value and g mNL3_i And g dsNL3_i Is with transconductance g m And conductance g ds And the related third-order nonlinear coefficient.
By injecting current into the ith operational amplifierMultiplying by the closed loop output impedance Z oCL_i Obtaining a third-order intermodulation quantity (IM 3) voltage v at the output of each stage IM_i . Third order intermodulation quantity (IM 3) frequency f of ith stage IM3 Position v IM_i Is represented by formula (3).
In formula (3), G LOOP Is the loop gain of the operational amplifier. It is assumed that the two non-linear terms add without regard to their relative phases and that only one term dominates in each frequency interval.
Will v IM_i Multiplying by TF i→out (open-loop transfer function from the i-th stage operational amplifier output end to the top-level output end of the multi-stage operational amplifier) inside the operational amplifier, and third-order intermodulation quantity v of the i-th stage operational amplifier output end IM_out_i As shown in formula (4). For the ith stage, TF i→out Equal to the transconductance g at the frequency of the third-order intermodulation quantity (IM 3) of each stage of operational amplifier after the ith stage m_j And open loop output impedance Z oOL_j Is a cumulative of (a):
adding the third-order intermodulation quantity of the output end of each stage of operational amplifier to obtain the total output third-order intermodulation quantity v IM_out_TOT As in equation (5).
Thus, the output of each stage of the operational amplifier and the total output third-order intermodulation quantity (IM 3) can be obtained, and the influence of the output third-order intermodulation quantity (IM 3) of each stage of the operational amplifier on the total output third-order intermodulation quantity (IM 3) can be judged.
Step 1 simulates the nonlinear coefficient g of the ith stage of a transconductance amplifier (OTA) in an open loop state mNL3_i And g dsNL3_i The method of (2) is as follows: equation (6) is derived from equation (3), and the gain G (ω) of each stage is rewritten to G m_i ·|Z o_i (ω) |. As can be seen from (6), when the single-stage amplifying circuit is loaded with low impedance, its transconductance g m Nonlinearity is dominant because the output swing is small at this time. Conversely, when the load impedance is higher, a larger output swing causes conductance g ds Non-linearities predominate. If the single-stage output load resistance is 1Ω, equation (6) may be approximated as equation (7). With amplitude of oscillation A 1_i And A 2_i To simulate the output intermodulation quantity (|v) of the circuit by the input double-tone signal of (a) IM_out_i I) can be extracted by inverting equation (7) mNL3_i The coefficients are shown in formula (8).
Nonlinear coefficient g dsNL3_i The same simulation method can be used. At a sufficiently low frequency Z o_i (omega) is the parallel output impedance r of the transistor o Typically on the order of kilohms. Bringing the result of formula (8) into formula (7) to obtain
And (3) carrying the nonlinear coefficients calculated in the formulas (8) and (9) into formulas (1-5) to calculate so as to obtain the third-order intermodulation quantity (IM 3) output by each stage of the operational amplifier and the total output third-order intermodulation quantity. The correctness and the precision of the nonlinear analysis method applied to the multistage operational amplifier are verified by comparing the simulation result of the actual circuit. The comparison result is shown in FIG. 2.
Fig. 2 reflects the amount of third order intermodulation (IM 3) generated by two input two-tone signals of power-20 dBm at a 1MHz frequency offset versus the frequency of the first of these signals. The difference between the calculated and simulated values is mostly around 1dBm, and the maximum difference does not exceed 2dBm. The third order intermodulation quantity (IM 3) calculated for each stage is also seen in fig. 2, representing the distortion of each stage, and is analyzed to see:
1) The last stage (third stage) determines distortion below 400 MHz.
2) In addition to this, the distortion of the first stage dominates.
3) When the first stage begins to dominate, the overall output third order intermodulation amount (IM 3) begins to decrease with frequency.
4) The distortion of the total output is independent of the second stage.
The nonlinear analysis method provided by the invention finds out which level of distortion is dominant in the operational amplifier, and provides a simpler and more effective method for optimizing the linearity of the multi-stage operational amplifier.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the invention, and it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (1)
1. A nonlinear analysis method applied to a multistage operational amplifier, comprising the steps of:
1) Calculating or simulating to obtain distortion term coefficients of each stage of the multistage operational amplifier in an open loop state;
2) Simulating to obtain the amplitude-frequency relation of the input and the output of each stage of the multistage operational amplifier in a closed loop state;
3) Calculating a closed loop output impedance at the third order intermodulation product frequency by dividing the open loop output impedance by the loop gain;
4) Calculating to obtain the output of each stage of the multi-stage operational amplifier and the total output third-order intermodulation quantity, so as to judge the influence of the output third-order intermodulation quantity of each stage of the multi-stage operational amplifier on the total output third-order intermodulation quantity;
in the step 1), the transconductance nonlinear term coefficient g of the ith stage operational amplifier in the open loop state is obtained through calculation or simulation respectively mNL3_i And outputting a nonlinear term coefficient g of the conductance dsNL3_i ；
The step 4) is specifically as follows:
first, the ith operational amplifier inputs two amplitudes A 1_i And A 2_i And the frequencies are omega respectively 1 And omega 2 The frequencies of the two third-order intermodulation products in the output current of the ith operational amplifier are respectively 2 omega 1 -ω 2 And 2ω 2 -ω 1 The method comprises the steps of carrying out a first treatment on the surface of the The injection current of the ith operational amplifier is the sum of nonlinear current caused by transconductance of the ith operational amplifier and nonlinear current caused by conductance, the injection current of the ith operational amplifier is multiplied by the closed loop output impedance of the ith operational amplifier to obtain the third-order intermodulation amount voltage injected by the ith operational amplifier, then the third-order intermodulation amount voltage injected by the ith operational amplifier is multiplied by an open loop transfer function from the output end of the ith operational amplifier to the top-layer output end of the multistage operational amplifier to obtain the third-order intermodulation amount of the output end of the ith operational amplifier, and finally the third-order intermodulation amount of each stage operational amplifier output end is accumulated to obtain the total output third-order intermodulation amount, so that the influence of the third-order intermodulation amount of each stage output of the multistage operational amplifier on the total output third-order intermodulation amount is judged.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101917169A (en) * | 2010-08-05 | 2010-12-15 | 复旦大学 | High-bandwidth low-power consumption frequency-compensation three-stage operational amplifier |
| CN102611400A (en) * | 2012-02-09 | 2012-07-25 | 东南大学 | High-gain single-stage operational transconductance amplifier |
| CN106656180A (en) * | 2016-10-18 | 2017-05-10 | 东南大学 | Calibration circuit and calibration method applied to input kickback non-linearity of SHA-less analog-to-digital converter |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101917169A (en) * | 2010-08-05 | 2010-12-15 | 复旦大学 | High-bandwidth low-power consumption frequency-compensation three-stage operational amplifier |
| CN102611400A (en) * | 2012-02-09 | 2012-07-25 | 东南大学 | High-gain single-stage operational transconductance amplifier |
| CN106656180A (en) * | 2016-10-18 | 2017-05-10 | 东南大学 | Calibration circuit and calibration method applied to input kickback non-linearity of SHA-less analog-to-digital converter |
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