Is there any relationship between the cutoff frequency and the resonant frequency? Is the transmitted power the highest when it is in resonance?

QWE4562009

Is there any relationship between the cutoff frequency and the resonant frequency? Is the transmitted power the highest when it is in resonance? [Copy link]

 

Is there any relationship between the cutoff frequency and the resonant frequency? Is the transmitted power the highest when it is in resonance?

maychang

For a single LC tank, the output voltage of the LC tank is maximum (or minimum) when the input signal frequency is exactly the resonant frequency. The cutoff frequency refers to the frequency when the output voltage is 0.707 times the maximum (or minimum) value. The cutoff frequency determines the bandwidth of the bandpass (or bandstop) filter.

maychang

The resonant frequency and cutoff frequency of the LC circuit are independent of the input signal and are inherent characteristics of the LC circuit, determined by the inductance, capacitance and equivalent resistance of the LC circuit.

maychang

How to know the maximum gain?

You can measure the inductance, capacitance and equivalent resistance and then calculate them, or you can change the input signal frequency and measure the "maximum gain".

maychang

“Is -3dB expressed in logarithms?”

It is a logarithmic method.

QWE4562009

maychang posted on 2019-12-19 10:11 For a single LC circuit, the output voltage of the LC resonant circuit is the maximum (or the minimum) when the input signal frequency is exactly the resonant frequency. The cut-off frequency refers to the output voltage...

It's all about the frequency of the input signal.

maychang

QWE4562009 posted on 2019-12-19 10:35 They are all based on the frequency of the input signal

"Maximum", "minimum", "-3dB"... refer to the input signal frequency.

However, the "resonance frequency" and "cut-off frequency" have nothing to do with the input signal frequency. Without input signal, the resonant frequency remains the same value, which is completely determined.

QWE4562009

maychang posted on 2019-12-19 10:16 “Is -3dB expressed in logarithms?” It is expressed in logarithms.

How are 0.707 and -3DB converted? -3DB=LgX?

QWE4562009

maychang posted on 2019-12-19 10:52 “Maximum”, “minimum”, “-3dB”…are for the input signal frequency…

The cutoff frequency should be related to the input frequency. When it reaches this frequency, the signal will attenuate immediately.

maychang

QWE4562009 posted on 2019-12-19 12:10 How is 0.707 and -3DB converted? Is -3DB=LgX?

The definition of "Bell" is the common logarithm of the ratio of two powers, that is, lg(P2/P1).

"Decibel" is abbreviated as "decibel", recorded as dB, and is defined as one tenth of a Bel, that is, 10lg(P2/P1).

maychang

QWE4562009 posted on 2019-12-19 12:10 How is 0.707 and -3DB converted? Is -3DB=LgX?

-3dB, that is, 10lg(P2/P1) = -3, which is lg(P2/P1) = -0.3. From lg(P2/P1) = -0.3, take the antilogarithm and you get P2/P1 = 0.5, that is, P2 = 0.5P1.

maychang

QWE4562009 posted on 2019-12-19 12:11 The cutoff frequency should be related to the input frequency. When it reaches this frequency, the signal will attenuate immediately

As mentioned before: without input signal, the cutoff frequency remains the same. No matter how the input signal frequency changes (same or different from the resonant frequency, same or different from the cutoff frequency), the cutoff frequency will not change. Therefore, the cutoff frequency has nothing to do with the input signal frequency, and the cutoff frequency is determined by the parameters of the LC filter circuit itself.

maychang

QWE4562009 posted on 2019-12-19 12:11 The cutoff frequency should be related to the input frequency. When it reaches this frequency, the signal will attenuate immediately

"At this frequency, the signal immediately attenuates"

No, the signal attenuation does not happen "instantly" but varies continuously.

QWE4562009

maychang posted on 2019-12-19 12:44 -3dB, that is, 10lg(P2/P1)＝-3, which is lg(P2/P1)＝-0.3. From lg(P2/P1)＝-0.3, find the antilogarithm and get P2/P1＝0. ...

What are P1 and P2 here?

lehuijie

QWE4562009 posted on 2019-12-19 14:08 What are P1 and P2 here

Two power values, such as signal and noise.

maychang

QWE4562009 posted on 2019-12-19 14:08 What are P1 and P2 here

"What are P1 and P2 here?"

Two power values need to be compared, such as output power and input power, or power at a resonant frequency and power at a cutoff frequency.

QWE4562009

maychang posted on 2019-12-19 14:42 "What are P1 and P2 here?" Two power values that need to be compared, such as output power and input power, or resonant frequency...

Is it output P2/input P1?

Why do some of them show 20lg instead of 10lg?

QWE4562009

maychang posted on 2019-12-19 12:44 -3dB, that is, 10lg(P2/P1)＝-3, which is lg(P2/P1)＝-0.3. From lg(P2/P1)＝-0.3, find the antilogarithm and get P2/P1＝0. ...

How can we express power in dB when the power is always in W? Isn't it also good to express W in scientific notation? And what parameter is dBm used to express?

QWE4562009

maychang posted on 2019-12-19 12:44 -3dB, that is, 10lg(P2/P1)＝-3, which is lg(P2/P1)＝-0.3. From lg(P2/P1)＝-0.3, find the antilogarithm and get P2/P1＝0. ...

Can I use the calculator that comes with my computer to calculate the antivalue? I tried this and it turns out that -0.3 is an invalid input, but 0.3 can be calculated. For example, first enter 0.9321, then press the Inv key, and finally press the ln key or log key. You can get 2.5398372393976584087036045094395 or 8.5526362194046651256482187750074.

maychang

QWE4562009 posted on 2019-12-23 10:46 How can we express power in DB when the power is in W? Isn't it also good to express W in scientific notation? And what parameter is dBm used to express?

The power unit has disappeared in (P2/P1).

I have posted a post discussing elementary functions. The independent variable of a logarithmic function must be a dimensionless pure number, and its result (function value) must also be a dimensionless pure number. Therefore, Bel (or decibel) is dimensionless.