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harmonics in balanced circuits

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Fractional-N

Fractional-N

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even order harmonics cancel

In any balanced circuit, odd harmonics circulate in a differential path, while even harmonics flow in a common-mode path.

is this phrase correct? why? sorry but I can't understand it :?:
 

What it means is that in an ideal differential circuit the even-order harmonics cancel and you are left with only the odd-order harmonics. Your common-mode signals will still see the even-order harmonics.
 

    Fractional-N

    Fractional-N

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the input output expression for a balanced circuit only have odd order terms (i mean like: x or x³ or x^5), right?
with the formula it is obvious that we dont have even harmonics. but i cant see how even harmonics CANCEL each other. can you explain.
additionally, the formula says that there is not any even harmonic in a balanced circuit, so how the common mode signals can see it?
the formula is from Razavi's book (RF microelectronics)

thanks for your reply :D but your reply is as ambiguous as the main sentence. :wink:
 

I'll give you a hint:

The differential signal is:
yp = x+ax^2+bx^3
ym =-x+a(-x)^2+b(-x)^3 = -x+ax^2-bx^3
where yp and ym are the positive and negative signals.

For the differential signal:
yd = yp-yp = x+ax^2+bx^3 - (-x+ax^2-bx^3) = x+ax^2+bx^3+x-ax^2+bx^3 =
2(x+bx^3)

For the common mode signal:
yc = (yp+ym)/2 = ax^2
 

    Fractional-N

    Fractional-N

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