[Repost] How to understand the high-frequency and low-frequency characteristics of components

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[Repost] How to understand the high-frequency and low-frequency characteristics of components [Copy link]

Let's talk about capacitors first. It is said that large capacitors have good low-frequency characteristics, and small capacitors have good high-frequency characteristics. Then, according to the fact that the size of the capacitive reactance is inversely proportional to the capacitance C and the frequency F, does a large capacitor not only have good low-frequency characteristics, but also better high-frequency characteristics? Because the higher the frequency, the larger the capacity, the lower the capacitive reactance, and the easier it is for high frequencies to pass through large capacitors, but from the slow charging and discharging speed of large capacitors, it seems that high frequencies are not easy to pass through. Isn't this a contradiction?

First of all, high frequency and low frequency are relative. If the frequency is too high, then it doesn't make sense to make the capacitance of the capacitor larger, because, as we all know, the coil is an inductor, which blocks high frequencies. The higher the frequency, the greater the blocking effect. Although the inductance is small, large-capacity capacitors generally have longer pins and larger plates circled together. At this time, the equivalent inductance of the two pins of the capacitor has already played a great role in blocking high frequencies.

Therefore, high frequency is not easy to pass through large-capacity electrolytic capacitors with poor high-frequency performance, while sheet ceramic capacitors have an advantage in price and performance.

Similarly, does the greater the inductance, the greater the barrier to high frequency? No. In order to obtain a larger inductance, there must be as many and as large coils as possible, and these conductors are like countless plates of capacitors. If these plates happen to be close to each other (which is inevitable in the pursuit of more turns), the distributed capacitance will provide a path for high-frequency signals.

Therefore, for signals in different frequency bands, capacitors and inductors of appropriate capacity should be selected.

Let's analyze the high-frequency equivalent circuits of the three most commonly used passive components, resistors, capacitors, and inductors:

1. High-frequency resistors

The most common circuit element in low-frequency electronics is the resistor, which is used to reduce the voltage by converting some electrical energy into heat energy. The high-frequency equivalent circuit of the resistor is shown in the figure, where the two inductors L simulate the parasitic inductance of the leads at both ends of the resistor, and the capacitance effect must also be considered according to the actual lead structure; the capacitor C simulates the charge separation effect.

Resistor equivalent circuit representation

According to the equivalent circuit diagram of the resistor, the impedance of the entire resistor can be easily calculated:

[p=32, null, The figure below depicts the absolute value of the impedance of a resistor versus frequency. As you can see, the impedance of a resistor is R at low frequencies, but as the frequency increases and exceeds a certain value, the influence of parasitic capacitance becomes dominant, causing the impedance of the resistor to decrease. As the frequency continues to increase, the total impedance increases due to the influence of the lead inductance, which represents an open line or infinite impedance at very high frequencies.

The relationship between the absolute value of a typical 1KΩ resistor impedance and frequency

2. High-frequency capacitors

Flake capacitors are widely used in RF circuits. They can be used in many circuits such as filter frequency modulation, matching networks, and transistor bias. Therefore, it is necessary to understand their high-frequency characteristics. The high-frequency equivalent circuit of the capacitor is shown in the figure, where L is the parasitic inductance of the lead; a series equivalent resistor R1 is used to describe the lead conductor loss; and a parallel resistor R2 is used to describe the dielectric loss.

Capacitor equivalent circuit representation

The relationship between the absolute value of the impedance and the frequency of a typical capacitor can also be obtained. As shown in the figure below, due to the presence of dielectric loss and finite length leads, the capacitor shows the same resonant characteristics as the resistor.

A typical relationship between the absolute value of 1pF capacitor impedance and frequency

3. High frequency inductor

[p=32, null,[left]Inductors are less commonly used than resistors and capacitors. They are mainly used in transistor bias networks or filters. Inductors are usually made by winding a wire around a round conductor column. Therefore, in addition to considering the inductive characteristics of the inductor itself, it is also necessary to consider the resistance of the wire and the distributed capacitance between adjacent coils. The equivalent circuit model of the inductor is shown in the figure below. The parasitic bypass capacitor C and the series resistor R are the combined effects of the distributed capacitance and the resistor, respectively.

Equivalent circuit of high-frequency inductor

Similar to resistors and capacitors, the high-frequency characteristics of inductors are also different from the expected characteristics of ideal inductors, as shown in the figure below: First, when the frequency approaches the resonance point, the impedance of the high-frequency inductor increases rapidly; second, when the frequency continues to increase, the influence of the parasitic capacitance C becomes the main one, and the coil impedance gradually decreases.

The relationship between the absolute value of inductor impedance and frequency

In short, in high-frequency circuits, the performance of wires together with basic passive devices such as resistors, capacitors and inductors is obviously different from the characteristics of ideal components. Readers can find that the constant resistance value at low frequency shows a second-order system response with a resonance point at high frequency; at high frequency, the dielectric in the capacitor produces loss, causing the impedance characteristics of the capacitor to be inversely proportional to the frequency only at low frequencies; at low frequencies, the impedance response of the inductor increases linearly with the increase of frequency, begins to deviate from the ideal characteristics before reaching the resonance point, and finally becomes capacitive. The characteristics of these passive components at high frequencies can be described by the quality factor mentioned above. For capacitors and inductors, for the purpose of tuning, it is usually desired to obtain the highest possible quality factor.