[Operational amplifier parameter analysis and LTspice application simulation] Come to LTspice|Calculate the RMS value of the amplifier circuit noise...
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Opening words:
The book "Operational Amplifier Parameter Analysis and LTspice Application Simulation" took more than half a year to write, and the preparations for publication are now underway. The original intention of writing this book is to provide effective guidance and help for analog electronics engineers in amplifier design and use, and strive to make this book a standing reference book for engineers.
This book is based on the author's collection of amplifier parameter data. From more than 600 projects supported, the author has selected more than ten representative amplifier design cases and deeply analyzed the application of parameters. In addition, with more than 50 LTspice simulation circuits, the parameter characteristics are verified with the actual operational amplifier model. This book can also help engineers master the use of LTspice simulation tools, efficiently and reliably ensure the progress of project development in daily work, and improve the working skills of analog electronic engineers.
Fortunately, Mr. Guo Jian, an expert in the field of amplifiers at ADI, recognized the content and creative concept of the book and wrote a preface for it. At the same time, in recent exchanges with industry insiders, we learned that many engineers not only need paper books as tools, but also hope to obtain electronic versions for convenient and flexible reading. Therefore, this public account will regularly excerpt exciting content such as amplifier parameter analysis, practical cases, LTspice simulation verification, etc. from the book to facilitate engineers to learn and interact.
A single-channel amplifier usually has only 5 pins and may seem like a very simple device, but as a core device for analog signal processing, it is necessary to evaluate the matching degree between design requirements and amplifier parameters in detail in the application. As the opening article of the official account, this article presents the tedious calculation method of the amplifier noise RMS value, and how to use LTspice simulation to easily achieve effective evaluation of the noise RMS value . Welcome to discuss and share.
1. Amplifier noise types and analysis
The noise inside the amplifier is composed of 1/f noise and broadband noise. The two are uncorrelated, so the total noise is calculated by RMS.
(1) Flicker noise is also called 1/f noise. It is ubiquitous in nature and human life. In amplifiers, it is mainly related to the imperfect semiconductor crystal structure and has the following characteristics:
1) 1/f noise decreases as frequency increases
2) Each frequency multiple (or decade) contains the same power within its bandwidth.
The 1/f noise RMS values of the amplifier voltage and current are expressed in Equations 2-51 and 2-52, respectively.
Where en, In are the measured 1/f noise RMS values, Ke, Ki are proportional constants, and fmax, fmin are the upper and lower frequency limits of the frequency band.
(2) Broadband noise: noise with a constant noise power within a bandwidth, that is, the noise density is constant. Broadband noise, shot noise, and resistor thermal noise can be approximately considered white noise. It is called white noise because it is similar to white light. In white light, all colors are used in equal amounts.
The broadband noise RMS values of the amplifier voltage and current are expressed in Equations 2-53 and 2-54 respectively.
Among them, ewn, Iwn, is divided into voltage noise density and current noise density.
As shown in Figure 2.77, the amplifier noise and frequency characteristics, the X-axis represents frequency, the unit is Hz, the Y-axis represents voltage noise density, or current noise density, the unit is usually nV/√HZ, pA/√HZ. In the low frequency range, 1/f noise is the main component of the total noise, and in the high frequency range, broadband noise is the main component of the total noise. Extend the 1/f noise curve to high frequency and the broadband noise to low frequency. At the intersection of the two, the 1/f noise and broadband noise have the same amplitude. The frequency of this point is called the "corner frequency" fnc. The total noise at this point is √2 times the broadband noise.
Figure 2.77 Amplifier noise frequency characteristics
The position of fnc is related to the total noise calculation and needs to be calculated accurately. The steps are as follows:
(1) Calculate the square of the 1/f noise at the lowest frequency, subtract the square of the broadband noise from it, and multiply the result by the lowest frequency to get the square of the 1/f noise at that frequency.
(2) Divide the square value of the lowest frequency 1/f noise by the square value of the broadband noise, and the result is fnc.
[ Amplifier voltage noise calculation example ] Taking the voltage noise of ADA4077 as an example, the RMS value of the total noise from 1Hz to 1KHz is calculated using 1/f noise density and broadband noise density.
As shown in Figure 2.6, the voltage noise density of ADA4077 at 1Hz is 13nV/√Hz, and the voltage noise density at 1KHz is 6.9nV/√Hz. 1Hz can be regarded as the lowest frequency of voltage 1/f noise, and the noise of 1KHz can be regarded as broadband noise, and the corner frequency can be calculated.
Figure 2.6 ADA4077 noise and isolation performance
Substituting the corner frequency, 1/f noise density, and broadband noise density into equations 2-51 and 2-53, the total noise RMS value from 1Hz to 1KHz can be calculated as:
2. Noise analysis of amplifier circuits
The total noise presented in the amplifier working circuit includes current noise, voltage noise, and resistance noise. First, it is necessary to obtain the main noise factor based on the actual circuit analysis, and then regard the influence of the main noise factor as an approximate evaluation of the total noise.
[ Example of noise analysis of amplifier circuit ] As shown in Figure 2.78, when the signal is introduced from point A, the circuit is regarded as an inverting amplifier circuit with a gain of -R2/R1. When the signal is introduced from point B, the circuit is regarded as a non-inverting amplifier circuit with a gain of 1+R2/R1, and the noise gain is 1+R2/R1. The total noise RMS value en_RTI converted to the input end of the circuit is formula 2-55:
Among them, enR1, enR2, and enR3 are the thermal noise of resistors R1, R2, and R3, enA is the voltage noise of the amplifier, and In+ and In- are the current noise of the in-phase and inverting input terminals of the amplifier. In the RMS calculation, the influence of In-, enR1, and enR2 can be ignored, and the total noise RMS value converted to the input terminal is approximately as Equation 2-56.
Figure 2.78 Amplifier circuit noise model
As shown in formula 2-56, the influence of voltage noise density is usually given priority. The current noise density is pA/√Hz, which is usually relatively small. The influence of current noise can only be reflected when the resistance value of R3 is greater than en/In (calculated by broadband noise density), otherwise the influence of current noise can be ignored. Only when the resistance value of resistor R3 is close to en/In (calculated by broadband noise density), the influence of R3 thermal noise is more obvious.
As shown in Figure 2.79, when the ADA4807 is in a 25°C environment and the operating voltage is ±5V, the noise at 100KHz is considered as broadband noise. The voltage broadband noise is 3.1nV/√Hz, and the current broadband noise is 0.7pA/√Hz. Therefore, when the R3 resistance is much smaller than 4.4KΩ, the voltage noise is the main component, when the R3 resistance is 4.4KΩ, the thermal noise is the main component, and when the R3 resistance is much larger than 4.4KΩ, the current noise is the main component. The data sheet also provides a voltage 1/f noise corner frequency of 29Hz and a current 1/f noise corner frequency of 2KHz.
Figure 2.79 ADA4807 current noise and voltage noise
Use ADA4807 to implement the amplifier circuit in Figure 2.78. The resistor R1 is 100Ω, the resistor R2 is 900Ω, and the resistance of R3 is set to 0Ω, 4.4KΩ, and 440KΩ respectively to calculate the total input noise of the circuit. Among them, 10Hz is the lowest frequency point of 1/f noise, and the noise of 100KHz is broadband noise. The noise density at the input end is evaluated under various conditions, as shown in Table 2.8.
Table 2.8 Effect of source impedance R3 on main noise
According to the three cases in Table 2.8, the total circuit noise is calculated respectively, and the noise analysis is compared using LTspice as follows:
(1) As shown in Figure 2.80, when the source impedance is 0Ω, the ADA4807 voltage noise is the main influencing factor, and the noise converted to the output is:
Figure 2.80 Noise simulation circuit with source impedance of 0Ω
By calculating the corner frequency of the voltage noise , it is 25Hz, which is close to the 29Hz provided in the data sheet of Figure 2.79. When the source impedance is 0Ω, the RMS value of the output noise voltage generated by ADA4807 within 10Hz to 100KHz is approximately 9.8037uV.
The noise simulation results are shown in Figure 2.81. The output noise voltage RMS value is 10.27uV, and the impact of ADA4807 voltage noise is approximately 95%.
Figure 2.81 ADA4807 output noise simulation results when source impedance is 0Ω
(2) As shown in Figure 2.82, when the source impedance is 440KΩ, current noise is the main influencing factor, and the noise converted to the output is:
Figure 2.82 Noise simulation circuit with source impedance of 440KΩ
The corner frequency of the calculated current noise is 2030Hz, which is close to the 2KHz provided in the data sheet of Figure 2.79. When the source impedance is 440KΩ, the RMS value of the output voltage noise generated by ADA4807 within 10Hz to 100KHz is approximately 1.025mV.
The noise analysis results are shown in Figure 2.83. The output noise RMS value is 1.0557mV, and the impact of ADA4807 current noise is approximately 91%.
Figure 2.83 ADA4807 output noise simulation results when the source impedance is 440KΩ
(3) As shown in Figure 2.84, when the source impedance is 4.4KΩ, the thermal noise of the resistor is the main noise, and the noise converted to the output is:
In the range of 10Hz to 100KHz, the RMS value of the output noise voltage caused by the resistor thermal noise is 26.53μV.
Figure 2.84 Noise simulation circuit with source impedance of 4.4KΩ
The noise simulation results are shown in Figure 2.85. The output noise RMS value is 31.191μV, and the influence of resistor thermal noise is about 85%.
Figure 2.85 ADA4807 output noise simulation results when the source impedance is 4.4KΩ
In summary, the resistance value of the resistor should be controlled in the precision measurement circuit. The single subject noise factor evaluation is applicable to low source impedance and high source impedance modes. When the source impedance is close to en/In (calculated by broadband noise density), the use of the single subject noise factor evaluation will lead to increased deviation in the evaluation results.
By verifying the theoretical calculation through simulation, we can more clearly understand the influence of the amplifier voltage noise, current noise, and resistance noise in the amplifier circuit. In the noise analysis of the amplifier circuit, it is often necessary to iterate multiple sets of configuration parameters. If we rely solely on theoretical calculations, even if we exclude errors caused by human factors, the workload cannot be ignored. Therefore, using LTspice for simulation is undoubtedly the best choice.
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