Question

A device produces a square wave current waveform as depicted below i (mA) 10 5 t (sec) fur w It is desired to obtain the triangular voltage waveform shown below v (V) 12 < 1 1 1 3 4 t (sec) What device/element would you use and what are its characteristics including its initial state? Hint: one definition of the square wave is simply the sign function of a sinusoid: x(t) = sign(sin[2nft]) which will be 1 when the sinusoid is positive, -1 when the sinusoid is negative, and 0 at the discontinuities. Here, f is its frequency. The triangle wave can also be expressed as the integral of the square wave: y(t) = 5 x(t) dt.

Answer 1

Given problem has been solved with proper explanation and calculations. To understand this problem, a basic knowledge of capacitor is required. If you have any doubt, please comment.

A device produces a square ware current ware form depicted below i (mA) 10 A * t (see) 2 3 4 -10 It is desired to obtain the triangulay voltage wave form shown below. U (volt) & 12 3 + 3 * t (820) 1 2 4 S wave can be What device / element would you use and what are its characteristics including its final stale? By integrating a square ware, a. triangular generated. Squeare Triangular ware Integration We know that, the relation between voltage and current of a capacitor is & (t) = 12 ) i (t) at ware t

u(t) = nl - < [ ] ict) df + sic) de] & J (Ct) at t si(t) at the sict) at 0 - 0 Initial state / Initial voltage of capacitor. the current ware form voltage acerous capacitor. By entegrating we can get the vo So, here A i(t) = 10x103 sign (aim (271 ft)) where, at f = 1/2 = 2 a0.5 Hz. (4) - A) 10 2 3 14 5 T si(t) = = 0.01 sign (sim im (TT+)) A sim (Tit) > 0 0.03 A sim (Tt) co 0.01 A ܕܝ "Sign [x] = 1; x70 : -I XCO

re (4) s ict) at it recom) с Now, initial state : (+) 12 3 t (see) + 2 3 4 210-) = 3 V Here, the initial state / initial vo voltage of the capacitor is 3v. To obtain the desired triangular ro roltage wave form capacitor will be used. And the initial state of capacitor musst be 3 V