[SOLVED] Is Cutoff frequency derived from Maximum power theorem?

[debasish.deka]

As I was trying to understand a simple RC first order filter (with voltage measured across the capacitor) which tells cutoff frequency occurs at Zc=R (Zc being the impedance of the capacitor)

I found it similar to the maximum power theorem (which tells maximum power is transmitted to load when impedance of load equals the impedance of source).
I want to know whether these two theories bear any relation?

 

[chuckey]

None what so ever.
Frank

 

[debasish.deka]

Then on what basis is the cut off frequency chosen ? I want to know this because the output changes gradually at -20dB, so why is cut off frequency chosen to be at Zc=R ? It sheer inquisitiveness.

 

[FvM]

Cutoff frequency refers to 3 dB attenuation point of frequency characteristic. You get it by calculating the (complex impedance) voltage divider.

 

[Venkadesh_M]

You need not to go with maximum power transfer... That is top of the frequency response curve.. but for calculating cuttoff points you just need the 3db points...
In your concern you can use this method for calculating frequency in which the maximum power transfer occurs (Resonant frequency) . . . but not 3db frequencies....

 

[LvW]

Then on what basis is the cut off frequency chosen ? I want to know this because the output changes gradually at -20dB, so why is cut off frequency chosen to be at Zc=R ? It sheer inquisitiveness.

For your first-order circuit the cut-off frequency can be chosen at that frequency where |Zc|=R.
Of course, this is identical to a magnitude that is 3 dB down.
Another parameter that can be used for cut-off definition is the phase shift.
In your case, the phase shift at the cut-off is -45 deg.
Note: For second-order filters, the phase shift at the pole frequency (not identical but a measure of the cut-off frequency) is -90 deg.

 

[debasish.deka]

Yes I understand 3dB down refers to |Zc| = R in a passive RC circuit with output measured across the capacitor, but I was trying to arrive at a sort of axiom - the fundamental principle. As far as 3dB is concerned standard definition says it is based on the RC circuit as " -3dB is the point at which output is 1/sqrt(2) of the input". Now this definition is obtained when |Zc| = R. So what I found is this 3dB point definition is derived from RC LPF rather than the other way round - "cut off frequency refers to frequency at which Vout = 0.707 x Vin". I think it should be defined as "cut off frequency refers to frequency at which |Zc| = R".
But I think your definition is better keeping higher order filters in mind.
Now my basic query - Is maximum power theorem somewhere related to cutoff frequency ? I may be wrong but just I though this way. Maximum power theorem tells maximum power is transmitted when Rin = Rload similar to the LPF cutoff frequency definition.

 

[FvM]

Maximum power theorem tells maximum power is transmitted when Rin = Rload similar to the LPF cutoff frequency definition.

Equality of impedance absolute value has nothing to do with Rin = Rload.

 

[LvW]

But I think your definition is better keeping higher order filters in mind.

Exactly - that`s the point!
In general, the definition (better; common agreement) has nothing to do with equality of components or power transfer.
It is simply meaningful to define the edge of the passband based on some properties that can be easily verified by measurements.
Thus, in many cases it is the 3-dB point - however, for some filter functions (Chebyshev or elliptic/Cauer) the passband is NOT defined using the 3dB criterion.
In these cases it is the specified ripple within the passband that defines the band edges (for example: 0.1 dB or 1 dB).

 

[debasish.deka]

Ok, okay I understood. Thanks all :smile: for clearing the air :smile: