- #1
Forcefedglas
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Homework Statement
For an upcoming lab I've been asked to build a circuit to convert a square wave (vi(t))e into a sine wave (v0(t)) by selecting appropriate resistor/capacitor values for the circuit below (from what I know, it's impossible to produce an accurate sine wave with just this, I assume that I just have to do the best I can). Searching around online has only given me some qualitative explanations so I'm looking for a circuit analysis based explanation on how this is supposed to work.
$$v_i(t)= (-1)^n), nT_0<t\leq(n+1)T_0, n=...-2,-1,0,1,2..., T_0=\frac{1}{100}secs$$
Homework Equations
$$a_0=\frac{1}{T}\int_{0}^{T}f(t)dt$$
$$a_n=\frac{2}{T}\int_{0}^{T}cos(nw_0t)f(t)dt$$
$$b_n=\frac{2}{T}\int_{0}^{T}sin(nw_0t)f(t)dt$$
$$V=IZ$$
The Attempt at a Solution
I started by calculating the Fourier series, which I believe works out to be $$-\sum_{k=1}^{\infty}\frac{8}{(2k-1)\pi}sin(\pi (2k-1)t)$$
Then I attempted to get an equation for v0(t) in terms of vi(t). Simplifying the resistor and capacitor in parallel then applying voltage division gave:
$$v_0(t)=\frac{R_2}{R_1+R_2+jR_1R_2\pi nC}v_i(t)$$
May have made a mistake in there somewhere but either way from this point on I don't have a clue on how to proceed, I thought about making the denominator real but I'm not seeing how that would help. Any tips will be appreciated, thanks!
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