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

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The discussion focuses on representing a triangle wave for input voltage in a specific circuit from Agarwal's Foundations of Analog and Digital Circuits. The circuit behavior changes based on the value of v_0, with different equations for when v_0 is less than or greater than zero. A periodic triangle wave function, f(t)=|t|, is proposed, but it is noted that this representation may not align with the exercise's intent. Corrections to the expressions for v_0 reveal a missed factor, leading to a revised understanding of the relationship between v_i and v_0. Ultimately, the participants explore the flexibility of substituting different functional forms for v_i in the context of the problem.
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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.
1724224917611.png


Here is my own picture of the circuit with circuit variables

1724224998144.png


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?
 
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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.

##\ ##
 
Last edited:
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?
 
zenterix said:
what exactly the functional form of the input voltage vi is
Would you say that if the exercise mentioned 'sine wave' instead of 'triangle' wave ?

##\ ##
 
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