Res_Notes - EE201.3 Frequency Effects – Series&...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ω L at very low frequencies, ( ω ⇒ 0, j ω L ⇒ 0) Z = R ∠ 0 Ω at very high frequencies, ( ω ⇒ ∞ , j ω L ⇒ ∞ ) Z = ∞∠ 90 Ω Define ω c (f c ) when |Z R | = |Z L | ⇒ R = ω c L; ω c = R/L = τ-1 when ω = ω c = R/L Z = R + j(R/L)L = R(1 +j1) = 1.414R ∠ 45 Ω when ω = 0.1 ω c Z = R + j(R/10L)L = R(1 +j0.1) = 1.005R ∠ 5.7 Ω when ω = 10 ω c Z = R + j(10R/L)L = R(10 +j1) = 10.04R ∠ 84 Ω For instance… for a 10K Ω 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 ω L ( ) R + j ω L ∗ 1 j ω L 1 j ω L ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ = R R j ω L + 1 = R 1 R j ω L + 1 ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ = R 1 1 − j 1 ω L R ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ When ω is very low (as ω⇒ 0, 1/ ω⇒∞ ) Z ≅ R/(1 -j ∞ ) = ∠ 90 Ω . When ω is very high (as ω⇒∞ , 1/ ω⇒ 0) Z ≅ R/(1-j0) = R ∠ Ω . Again, cutoff frequency, ω c , is when ⎢ Z R ⎢ = ⎢ Z L ⎢ and ω c = R/L ; = τ-1 and Z = R/(1-j1) = 0.707R ∠ 45 Ω At ω = 0.1 ω c , Z = R/(1-j10) ≅ 0.1R ∠ 84 Ω , At ω = 10 ω c , Z = R/(1+j10) ≅ 0.995R ∠ 5.7 Ω . For instance… for a 10K Ω 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 ω L ( ) R + j ω L ∗ 1 j ω L 1 j ω L ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ = R R j ω L + 1 = R 1 R j ω L + 1 ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ = R 1 1 − j 1 ω L R ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ When ω is very low (as ω⇒ 0, 1/ ω⇒∞ ) Z ≅ R/(1 -j ∞ ) = ∠ 90 Ω . When ω is very high (as ω⇒∞ , 1/ ω⇒ 0) Z ≅ R/(1-j0) = R ∠ Ω . Again, cutoff frequency, ω c , is when ⎢ Z R ⎢ = ⎢ Z L ⎢ and ω c = R/L ; = τ-1 and Z = R/(1-j1) = 0.707R ∠ 45 Ω At ω = 0.1 ω c , Z = R/(1-j10) ≅ 0.1R ∠ 84 Ω , At ω = 10 ω c , Z = R/(1+j10) ≅ 0.995R ∠ 5.7 Ω . For instance… for a 10K Ω 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 ω C ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = R + 1 j ω C ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = R j ω C ( ) + 1 j ω C = 1 + j ω RC j ω C at very low frequencies, ( ω ⇒ 0, X C ⇒ ∞ ) Z ≅ ∞∠-90 Ω at very high frequencies, ( ω ⇒ ∞ , X C ⇒ 0) Z = R ∠ Ω Define ω c (f c ) when |Z R | = |Z C | ⇒ R = 1/( ω c C); ω c = 1/RC = τ-1 when ω = ω c = 1/RC, Z = R - j(R) = R(1 -j1) = 1.414R ∠-45 Ω when ω = 0.1 ω c Z = R - j(10R) = R(1 +j10) = 10.04R ∠-84 Ω when ω = 10 ω c Z = R + j(0.1R) = R(1 +j0.1) = 1.005R ∠-5.7 Ω For instance… for a 10K Ω resistor and 10mH inductor: For instance… for a 10K...
View Full Document

This note was uploaded on 09/25/2010 for the course EE 201 taught by Professor Linch during the Spring '10 term at University of Saskatchewan- Management Area.

Page1 / 13

Res_Notes - EE201.3 Frequency Effects – Series&...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online