"Operational Amplifier Parameter Analysis and LTspice Application Simulation" Reading Notes 4 - Beautiful Diamond

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"Operational Amplifier Parameter Analysis and LTspice Application Simulation" Reading Notes 4 - Beautiful Diamond [Copy link]

 

Chapter 3 of the book "Operational Amplifier Parameter Analysis and LTspice Application Simulation" is about special amplifiers, including four types of special amplifiers: instrumentation amplifiers, transimpedance amplifiers, fully differential amplifiers, and current sense amplifiers.

The instrumentation amplifier is a familiar three-op-amp structure differential amplifier. The integrated instrumentation amplifier integrates four resistors that need to be precisely matched inside the op amp, so it has a very high common-mode rejection ratio. The book uses typical chips and actual cases to introduce in detail the characteristics of the instrumentation amplifier, effective working configuration, offset and noise analysis, and methods to improve the common-mode rejection ratio.

Since I have designed a similar instrumentation amplifier before (built by myself using three op amps), I am familiar with most of the above contents. However, the book mentions a "diamond diagram", which I have never noticed in my previous work, so I have done some research and analysis on it.

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The definition of the diamond plot is: the relationship between the input common-mode voltage range and the output voltage of the instrumentation amplifier at a given gain. The method of using the diamond plot is as follows: put the rectangle formed by the input common-mode voltage range and the output voltage range of the designed amplifier into the diamond plot. If it does not exceed the diamond plot range, the circuit can work normally. If it exceeds the diamond plot range, the operation may be abnormal.

The following figure is the diamond diagram of the chip AD8221 under the conditions of power supply voltage of ±15V and gain of 1 (the colored lines in the figure are added by me). The red dotted line is a hypothetical amplifier operating range: the input common mode range is -10V~+10V, and the output voltage range is -10V~+10V. As can be seen in the figure, the four corners of the rectangle are beyond the diamond diagram range, so the circuit will not work effectively. If the input common mode voltage range is reduced as shown in the green dotted line, the circuit can work normally.

Obviously, the diamond plot can be used to easily determine the effective operating voltage range of the instrumentation amplifier. Considering that relying solely on the diamond plot provided by the datasheet cannot meet the ever-changing requirements of users, the book "Operational Amplifier Parameter Analysis and LTspice Application Simulation" also introduces a software that users can use to easily determine whether the design is reasonable.

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But my interest in the diamond plot is not only in its application, but more importantly, on what principle is the diamond plot obtained? If the chip datasheet does not provide a diamond plot, or the chip model used cannot be found in the application software, how can I obtain its diamond plot based on other parameters provided in the datasheet?

The typical structure inside the instrumentation amplifier is shown in the figure below. A1 and A2 are in-phase amplifier circuits that provide high impedance differential input. A3 and four resistors form a precision differential amplifier. When the four resistors are precisely matched, the gain of the differential amplifier is 1.

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The diamond plot is actually the input and output voltage amplitude limit of the instrumentation amplifier under a given power supply voltage. In the structure of the instrumentation amplifier mentioned above, the factors that can constitute the voltage amplitude limit are nothing more than the following four: the input voltage and output voltage limit of A1 and A2, and the input voltage and output voltage limit of A3. Let's discuss them one by one.

First look at the output voltage limit of A3 .

This is the simplest limitation, which is shown as two straight lines on the left and right sides of the diamond plot, which are the output voltage limit values of the instrumentation amplifier usually given in the datasheet.

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Next, look at the maximum allowable input voltage limits of A1 and A2 .

When the instrumentation amplifier is added with the common-mode and differential-mode voltages as shown in the figure, the voltage at the input of A1 or A2 is the sum of the common-mode voltage and half of the differential-mode voltage. One case is when the differential-mode input voltage is 0, in which case the output voltage must be 0 (assuming the common-mode rejection ratio of the instrumentation amplifier is extremely large). In the diamond diagram, the position of V _o = 0 is at its upper and lower vertices, so these two vertices are the limits of the common-mode voltage allowed to be input, which is equal to the maximum allowable input voltage of A1 or A2, which is the maximum allowable common-mode input voltage listed in the instrumentation amplifier datasheet.

When the differential input voltage is not equal to 0, the voltage obtained at the input of A1 or A2 is the sum of the common mode voltage and half of the differential mode voltage. This voltage cannot exceed the maximum allowable input voltage Vim of A1 or A2 _{, that is, |Vcm} | ₊ | Vd / 2 |≤| Vim |. If Vd _is written as the output voltage divided by the voltage gain _{Vo /} G , the above relationship becomes | Vcm |+| Vo _/ 2G | ≤| Vim |. If the less _{than or equal sign is changed to an equal sign, it is its} limit value. In the relationship between the input common mode voltage and the output voltage (that is, the coordinate system of the diamond diagram), it is a slash, and it is one of the candidates for the upper and lower pairs of slashes in the diamond diagram.

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Let's look at the maximum allowable output voltage limits of A1 and A2 .

As mentioned before, the input voltage of A1 or A2 is | V _cm |+| V _o /2 G |. Since the gain of the instrumentation amplifier is provided entirely by A1 and A2 (the gain of the differential amplifier A3 is equal to 1), the output voltage of A1 or A2 is | V _cm |+| V _o /2|, which is limited by the maximum allowable output voltage of op amps A1 and A2. We have reason to believe that the three op amps in the instrumentation amplifier have the same output voltage limit, so the maximum allowable output voltage of A1 and A2 in the above limit can be replaced by the maximum output voltage of A3, so there is | V _cm |+| V _o /2|≤| V _om |, where V _om is the maximum output voltage of the instrumentation amplifier given in the datasheet. Similarly, changing the less than or equal sign to an equal sign gives another candidate for the two pairs of diagonal lines above and below the diamond diagram.

The input voltage limit of A3 can be ignored for the following reasons: Due to the voltage division of the resistors, the input voltage amplitude of A3 is always smaller than the output amplitude of A1 and A2. Normally, the maximum allowable input voltage range of the op amp is similar to or even larger than its output voltage range. Therefore, after considering the output limits of A1 and A2, the input of A3 will not continue to be restricted.

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So far, we have obtained the method of four diagonal lines in the diamond diagram:

In the equations | V _cm |+| V _o /2 G |=| Vim _| and | V _cm |+| V _o /2|=| V _om |, substitute the positive and negative extreme values of the actual common-mode input voltage and output voltage according to the four quadrants of the diamond diagram, and then substitute the positive and negative limit values of the common-mode input voltage and output voltage of the instrumentation amplifier according to the quadrants, and you can get two straight line equations in each quadrant, and draw eight diagonal lines based on them. Combining the input common-mode voltage limit and output voltage limit in the datasheet, you can get two diamond diagrams, and the smaller diamond is the final diamond diagram.

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Based on the above analysis, we can also draw the following conclusions:

1. Since the range beyond the diamond diagram is always at the four corners of the actual input and output rectangle, it is not necessary to make a diamond diagram. The rationality of the design can be judged based on the description of the above equation alone.

Example: The designed chip is AD8221, the power supply voltage is ±15V, and the gain is 1. The designed amplifier operating range: the input common mode range is -10V~+10V, and the output voltage range is -10V~+10V. Check whether the design is reasonable.

According to the AD8221 datasheet, the input voltage under the above working conditions is limited to -13.1V and +13.8V, and the output voltage is limited to -13.8V and +13.6V. Substituting the above design working conditions into the above equations is as follows:

In the first quadrant, | V _cm |+| V _o /2 G |=10+10/2=15V, | V _im |=13.8V, | V _om |=13.6V, whichever is less than the design value. So this alone can be used to judge that this design is unreasonable. This is the red dotted box in the previous diamond diagram, which obviously exceeds the diamond diagram.

Reasonable design conditions can also be determined based on the constraints of AD8221: the worst constraint is that the input voltage is limited to -13.1V, which corresponds to quadrants 3 and 4 in the diamond diagram. If the output voltage amplitude is required to be ±10V, the absolute value of the common-mode input voltage must be less than 8.1V, which is the green dotted box in the previous figure.

2. In the above example, G = 1. If G>1, there is no effect on the equation | V _cm |+| V _o /2|≤| V _om |, but the equation | V _cm |+| V _o /2 G |≤| V _im | is easier to satisfy. So in an instrumentation amplifier with a gain greater than 1, the four diagonal lines of the diamond plot will be mainly determined by the output voltage limit of A1 or A2.

3. In order to make the gain of the integrated instrumentation amplifier start from 1, the gain of the differential amplifier of A3 is determined to be 1. However, from the previous analysis, if the amplification factor of A3 is greater than 1, first, the diagonal line of the diamond diagram is mainly determined by the output voltage limit of A1 or A2, and second, the differential mode voltage output of A1 and A2 will decrease. Therefore, the 4 diagonal lines of the diamond diagram will become flatter, or the operating voltage range of the instrumentation amplifier will be larger. It can be seen that in the instrumentation amplifier composed of three op amps, the gain should be placed in the differential amplifier at the back as much as possible.

chunyang

Great post!

人为现象

gmchen published on 2021-5-16 11:26 Based on the above analysis, we can also draw the following conclusions: 1. Since the range beyond the diamond diagram is always at the four corners of the actual input and output rectangle, ...

Good posts must come from experts, so if you come across something interesting, you must find out why.

怀想天空

I admire you so much!

qwqwqw2088

Can LTspice software simulate this kind of diamond diagram?

The four slashes determine the input and output voltage limits. It seems that the parameter settings are quite troublesome.