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Unformatted text preview: EE201.3 Frequency Effects Series & Parallel Resonance Denard Lynch Page 1 of 13 Nov 2008 R L in Series: Z = R + j L at very low frequencies, ( 0, j L 0) Z = R 0 at very high frequencies, ( , j L ) Z = 90 Define c (f c ) when Z R  = Z L  R = c L; c = R/L = 1 when = c = R/L Z = R + j(R/L)L = R(1 +j1) = 1.414R 45 when = 0.1 c Z = R + j(R/10L)L = R(1 +j0.1) = 1.005R 5.7 when = 10 c Z = R + j(10R/L)L = R(10 +j1) = 10.04R 84 For instance for a 10K resistor and 10mH inductor: EE201.3 Frequency Effects Series & Parallel Resonance Denard Lynch Page 2 of 13 Nov 2008 R L in Parallel Z = R ( ) j L ( ) R + j L 1 j L 1 j L = R R j L + 1 = R 1 R j L + 1 = R 1 1 j 1 L R When is very low (as 0, 1/ ) Z R/(1 j ) = 90 . When is very high (as , 1/ 0) Z R/(1j0) = R . Again, cutoff frequency, c , is when Z R = Z L and c = R/L ; = 1 and Z = R/(1j1) = 0.707R 45 At = 0.1 c , Z = R/(1j10) 0.1R 84 , At = 10 c , Z = R/(1+j10) 0.995R 5.7 . For instance for a 10K resistor and 10mH inductor: EE201.3 Frequency Effects Series & Parallel Resonance Denard Lynch Page 2 of 13 Nov 2008 R L in Parallel Z = R ( ) j L ( ) R + j L 1 j L 1 j L = R R j L + 1 = R 1 R j L + 1 = R 1 1 j 1 L R When is very low (as 0, 1/ ) Z R/(1 j ) = 90 . When is very high (as , 1/ 0) Z R/(1j0) = R . Again, cutoff frequency, c , is when Z R = Z L and c = R/L ; = 1 and Z = R/(1j1) = 0.707R 45 At = 0.1 c , Z = R/(1j10) 0.1R 84 , At = 10 c , Z = R/(1+j10) 0.995R 5.7 . For instance for a 10K resistor and 10mH inductor: EE201.3 Frequency Effects Series & Parallel Resonance Denard Lynch Page 3 of 13 Nov 2008 R C in Series: Z = R jX C = R j 1 C = R + 1 j C = R j C ( ) + 1 j C = 1 + j RC j C at very low frequencies, ( 0, X C ) Z 90 at very high frequencies, ( , X C 0) Z = R Define c (f c ) when Z R  = Z C  R = 1/( c C); c = 1/RC = 1 when = c = 1/RC, Z = R  j(R) = R(1 j1) = 1.414R 45 when = 0.1 c Z = R  j(10R) = R(1 +j10) = 10.04R 84 when = 10 c Z = R + j(0.1R) = R(1 +j0.1) = 1.005R 5.7 For instance for a 10K resistor and 10mH inductor: For instance for a 10K...
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 Frequency, Parallel Circuit

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