Combining equations to make one!

**chunkylumber111** · April 20th 2012, 01:27 PM

Hello this question is based on a transfer function problem and I have the following formulas and need to arrive at an equation for T/V_D in terms of k₀, k₁, k₂ and k_t

where E = V_D - V_M, I = Ek₁, T = k₀I, V_t = k_tT and V_m = k₂V_t

My attempt:

T = k₀I where I = Ek₁therefore T = k₀Ek₁ where E = V_D - V_M hence T = K₀(V_D - V_M)K₁

Also we know that T = V_t/k_t where V_t = V_M/k₂therefore T = V_M/(k₂k_t) hence V_M= Tk₂k_tand substituting V_M= Tk₂k_t into T = K₀(V_D - V_M)K₁

we have T = K₀(V_D - Tk₂k_t)K₁ expanding brackets: T = K₀K₁V_D - K₀k₁Tk₂k_tI've tried various rearragements of this but don't seem to come up with T/V_Dcan anyone show me where I'm going wrong?
I'm really stuck

Thanks!

**princeps** · April 20th 2012, 11:37 PM

$\frac{T}{V_D}=\frac{k_0 \cdot I}{E+V_M}=\frac{k_0 \cdot I}{\frac{I}{k_1}+k_2 \cdot V_t}=\frac{k_0 \cdot I}{\frac{I}{k_1}+k_2 \cdot k_t \cdot T}=$

$=\frac{k_0 \cdot I}{\frac{I}{k_1}+k_2 \cdot k_t \cdot k_0 \cdot I}=\frac{k_0}{\frac{1}{k_1}+k_2 \cdot k_t \cdot k_0}=\frac{k_1 \cdot k_0}{1+k_1 \cdot k_2 \cdot k_t \cdot k_0}$

**chunkylumber111** · April 21st 2012, 01:11 AM

Got it now, thanks for your help!

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