How do we represent a triangle wave for input voltage in this circuit?

[zenterix]

Homework Statement

Assuming the diode can be modeled as an ideal diode, and $R_1=R_2$, plot the waveform $v_0(t)$ for the circuit below assuming a triangle wave input.

Relevant Equations

Write an expression for $v_0(t)$ in terms of $v_i, R_1$, and $R_2$.

This problem is from Agarwal's Foundations of Analog and Digital Circuits.

Here is the circuit.

Here is my own picture of the circuit with circuit variables

If $v_0<0$ then we replace the diode with a short circuit and

$$v_i=i_1R_1$$

$$i_3=-i_1$$

$$v_0=0$$

If $v_0\geq 0$ then we replace the diode with an open circuit and

$$v_i=i_1R_1+i_1R_2=2Ri_1$$

$$i_1=i_2$$

$$v_0=i_1R_2=v_i\frac{R_2}{R_1}$$

At this point we would sub in an expression representing the triangle wave that is $v_i$.

I'm not sure exactly how this would be in this context. I have used a periodic triangle wave function defined as $f(t)=|t|$ on $t\in [-\pi, \pi)$ which I then expressed as a Fourier series.

For the purposes of this problem, how would I represent the triangle wave?

 

[BvU]

Hi,

Check your $v_0=i_1R_2=v_i\frac{R_2}{R_1}$

$f(t)=|t|$ is a triangle wave plus a constant voltage. That's not what the exercise composer intended.

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[zenterix]

You are right, I missed a factor of 2 in the denominator of the expression for $v_0$. Here is the correction

$$v_0=i_1R_2=v_i\frac{R}{2R}=\frac{v_i}{2}$$

$f(t)=|t|$ is indeed always positive but making this symmetric about the $x$-axis is just a question of offsetting by a constant, right?

In any case, it does not seem that the assumption about what exactly the functional form of the input voltage $v_i$ is is relevant to this problem.

We could sub in many different functional forms. It's just a substitution. Or maybe I am missing something?

 

[BvU]

what exactly the functional form of the input voltage v_i is

Would you say that if the exercise mentioned 'sine wave' instead of 'triangle' wave ?

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