advertisement

SINGLE-TIME-CONSTANT NETWORK STC Circuits Time constant τ = CR for an RC network; τ = L/R for an LR network. Example: Reduce the network to an STC network, and find its time constant. Thevenin Rth=(R1||R2+R3)||R4 Rth= Vth ∴τ = Rth ⋅ C = [ R4 || (( R1 || R2 ) + R3 )] ⋅ C Example: Reduce to a STC, and obtain τ. C1 VI + C2 R VO - Cth C th = C1 + C 2 ∴τ = R(C1 + C 2 ) Example: COMPENSATED ATTENUATOR USING SUPERPOSITION LPF HPF vo = vo1 + v o 2 τ = ( R1 || R2 )(C1 + C 2 ) Classification of STC Networks STC: HP “High-Pass” LP “Low-Pass” Examples: Low-Pass Type: High-Pass Type: FREQUENCY RESPONSE OF STC NETWORKS Low-Pass Networks T (S ) = Or output K = input 1 + ( S / ω 0 ) T ( jω ) = ω0 is cut-off frequency, which is constant. K 1 + j (ω / ω 0 ) ω0 = 1 τ τ = time constant Example: VO ( s) 1 / SC 1 1 1 = = = = VI ( s) R + 1 / SC 1 + SRC 1 + Sτ 1 + ( S / ω 0 ) | T ( jω ) |= K 1+ ( ω 2 ) ω0 φ (ω ) = − tan −1 (ω / ω 0 ) Let ω >> 1 ω0 ∴ | T ( jω ) |≈ K ω0 ω i.e. if ω doubles in value (an octave), |T(jω)| is halved. 20 log10 0.5 = −6dB / octave if ω increases by a factor of 10 (a decade), |T(jω)| drops to 1/10th of its value. 10 log10 0.1 = −20dB / decade High-Pass Network Vo ( s ) s /ω0 R sCR s = = = = Vi ( s ) R + 1 1 + sCR 1 + ( s / ω 0 ) s + ω 0 sC In general: T ( s) = Ks s + ω0 | T ( jω ) |= φ = tan −1 ( Kjω = jω + ω 0 ω0 ) ω K 1− j ω0 ω = K 1 + (ω 0 / ω ) 2