Analysis of the method of increasing input impedance of bootstrap circuit

In the process of circuit design, bootstrap circuits composed of bootstrap capacitors can often be used to improve some performance indicators of the circuit, such as increasing the input impedance of the circuit, improving the gain of the circuit, and expanding the dynamic range of the circuit. Here, I give an example of a bootstrap circuit to explain in detail how it increases the input impedance of the circuit.

A very common schematic diagram is as follows.

In the figure above, in order for the op amp to work properly in static state, a resistor of a certain value must be added between the in-phase input terminal and the ground. A simple analysis shows that a voltage series negative feedback is introduced here. People who are familiar with the working principle of the op amp can see at a glance that the input resistance of this circuit is:

Obviously, such input resistance is too small, so the current required by the amplifier circuit from the signal source will be relatively large, and the voltage drop of the internal resistance of the signal source will increase accordingly, and the signal voltage loss will naturally increase. Therefore, we have to find a way to increase its input resistance. At this time, we can set up a bootstrap circuit to effectively solve this problem. The solution is shown in the figure below:

By simply adding one more capacitor, the input resistance of this circuit is "very different now". Using the instantaneous polarity method, it can be determined that in addition to introducing a negative feedback by connecting R4 to the reverse input terminal, a positive feedback is also introduced by connecting R1 to the non-inverting input terminal. At this time, the two resistors R2 and R3 are connected in parallel. It should be noted that the selected values ​​of the capacitors (C1, C2) here are relatively large, and they are equivalent to short circuits relative to AC signals. The result of positive feedback causes the dynamic potential of the input terminal to increase accordingly. That is, this circuit that increases the dynamic potential of the input terminal through feedback is called a "bootstrap circuit".

Due to the good "AC-passing and DC-blocking" characteristic of capacitor C2, the voltage drop across R1 is (uP-uN). At this time, the current passing through resistor R1 is:

Let's take a look at the input resistance of this circuit and get the following equation:

Obviously, for this op amp, since deep negative feedback is introduced into the circuit, uP and uN are almost equal, then Ri will tend to a maximum value, the input resistance will be greatly improved, and the performance indicators of the circuit will be greatly improved.

Conclusion of this article: From this analysis, we can see that in the RC coupled amplifier circuit, it is often possible to introduce appropriate positive feedback at the same time as introducing negative feedback, so as to increase the input impedance of the circuit and effectively improve the performance indicators of the circuit.