LR03 alkaline battery.What is the role of negative feedback resistor in op amp circuit? Methods of connecting radio frequency resistors in parallel with equivalent capacitors

　　What role does the negative feedback resistor provided by electronic enthusiasts play in the op amp circuit? The method of connecting RF resistors in parallel with equivalent capacitors. High-power resistors used in RF and microwave frequency bands are mostly used in Wilkinson power dividers or combiners. For best performance, the 100 ohm isolation resistor used in the Wilkinson power splitter must have a small equivalent capacitance to reduce the impact on insertion loss. Additionally, if isolation resistors are used in a Wilkinson combiner, they need to absorb half of the input power at each input port. What is the role of negative feedback resistor in op amp circuit?

　　When the internal resistance of the signal source is large, adding a feedback resistor with the same resistance as the internal resistance of the signal source can reduce the output offset voltage and improve the following accuracy.

　　The ideal closed-loop gain of both voltage followers is equal to unity.

　　In a voltage follower, the influence of common mode rejection ratio will be enhanced. In addition, not connecting a resistor between the non-inverting terminal and the signal source is beneficial to reducing the steady-state error.

　　However, when the matching resistance is zero, the feedback resistance is required to be zero. When blockage occurs, the current in the feedback loop is large, which is not conducive to the protection of the input stage. Therefore, care should be taken during use.

　　A follower with a feedback resistor has a certain current limiting protection effect on the circuit when the circuit is blocked. This is its advantage. But the steady state error has increased a bit.

　　【Note】What is blockage?

　　The voltage follower is originally a non-inverting operational amplifier. One of the common characteristics of non-inverting operational amplifiers is that a common mode voltage is added to the non-inverting and inverting terminals.

　　Methods of connecting radio frequency resistors in parallel with equivalent capacitors

　　High-power resistors used in RF and microwave frequency bands are mostly used in Wilkinson power dividers or combiners. For best performance, the 100 ohm isolation resistor used in the Wilkinson power splitter must have a small equivalent capacitance to reduce the impact on insertion loss. Additionally, if isolation resistors are used in a Wilkinson combiner, they need to absorb half of the input power at each input port.

　　Separate resistors are often used in designing high power attenuators. At low frequencies, this is feasible; however, at high frequencies, the parasitics of the separate resistors can cause the attenuator to behave worse than expected.

　　High power resistors come in different shapes and sizes. The most common types of applications are: surface mount resistors, resistors with leads (with or without insulating housing), resistors with leads and insulating housing, and mounted on conductive flanges. The shapes of various high power resistors are as follows:

　　Specifications of high power resistors

　　The main parameters of high-power resistors include: resistance value, maximum power capacity (mostly at 100 degrees temperature), power-temperature curve and mechanical dimensions. In addition, the maximum or typical equivalent capacitance value also needs to be provided in some cases.

　　These two parameters, resistance and maximum power, are generally relatively well-defined and useful to designers. Relatively speaking, the parameter equivalent capacitance is relatively vague. In most cases, manufacturers do not provide the frequency at which the equivalent capacitance is measured and which test method is used.

　　There are many types of equivalent capacitance. The parallel equivalent capacitance refers to the capacitance formed by the radio frequency scattering field between the resistive film and the ground plane (Figure 2). Other equivalent capacitances, such as those between the input and output pads, are generally not considered as important because they have less impact on practical applications, especially at low frequencies.

　　So far, there is no standard for testing the equivalent capacitance of high power resistance above 1MHz. According to the MIL-STD202G standard, the recommended test frequencies for equivalent capacitance are: 60Hz, 120Hz, 1KHz, 10KHz and 1MHz.

　　Some people have pointed out that the equivalent capacitance measured at 1MHz must meet the MIL standard, but this capacitance information is of no use to designers who want it to work at 2.7GHz. The same situation applies to base station products operating in the GHz frequency range.

　　Test methods and extraction of equivalent capacitance

　　When high-power resistors are used in radio frequency and microwave frequency bands, they have the property of damaging transmission lines. Figure 3 is a lumped element model of a resistor and its high-frequency equivalent circuit model. The parallel capacitance in Figure 3 can be extracted by testing the S parameters. However, the type of test equipment, calibration technique, and dielectric constant of the material will all affect the test results.

　　In order to demonstrate the extraction process of equivalent capacitance more vividly, we used a 500W 50-ohm resistor with leads to create a sample as shown in Figure 4. The establishment of the reference plane in Figure 3 is achieved through the calibration and settings of the test instrument.

　　Test data and modeling data

　　In order to verify the parameter extraction process, we used MicrowaveOffice to build an EM resistance model. As shown in Figure 5, the S parameters obtained by EM analysis and the S parameters obtained by testing are marked together on an original Smith diagram. As can be seen from the figure, below 2.7GHz, the tested data and modeled data have a good correlation.

　　Calculation of equivalent capacitance

　　In order to obtain the parallel equivalent capacitance of the resistor, we need to use the value b, whose value at any frequency can be obtained directly from the diagram we gave as an example.

　　For example, as follows, we can find from the green line (test data): at 2.3GHz, b=1.083. Plugging this into the formula below gives us a value of 1.5pF for the equivalent capacitance.

　　If we follow the red line (modeled data) to get b, and then recalculate the equivalent capacitance at 2.3GHz, it is 1.55pF. These two data again show a good correlation between the test data and the modeled data.

　　In addition to the calculation of a single frequency point, we show the frequency sweep test results of parallel capacitors in Figure 6. The results also show that the S parameters obtained by the two methods are highly correlated.

　　High power resistors are widely used in power distribution circuits. The parallel equivalent capacitance (parallel end to ground) due to RF scattered fields between the resistive film and ground becomes an important design parameter. Typical values of equivalent capacitance are generally given measured at a frequency of 1MHz. However, in the GHz frequency band, a high-frequency equivalent capacitance value will be more meaningful for design.

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