Lecture #3. Charging / Discharging of Capacitor and Wave Converter. Rangkaian Pengisian dan Pengosongan Kapasitor dan Pengubah Gelombang

Transkripsi

1 Lecture #3 Charging / Discharging of Capacitor and Wave Converter Rangkaian Pengisian dan Pengosongan Kapasitor dan Pengubah Gelombang

2 Contents : Capacitor (review) Capacitor Charging (Pengisian Kapasitor) Capacitor Discharging (pengosongan Kapasitor) RC Integrator (Rangkaian Pengintergral RC pasif ) RC Differentiator (Rangkaian Pendifferensial RC pasif)

3 Kompetensi Dasar Menganalisis rangkaian pengisian dan pengosongan kapasitor dan penerapannya pada kehidupan Menganalisis rangkaian pengintergral RC pasif (Integrator) dan rangkaian pendifferensial RC pasif (Differensiator)

4 1. Kapacitor (Review) Capacitors are devices that store energy in an electric field. Capacitors are used in many every-day applications Electronic Instrument Camera flash units Capacitors are an essential part of electronics. Capacitors can be micro-sized on computer chips or super-sized for high power circuits such as FM radio transmitters.

5 Capacitors come in a variety of sizes and shapes. Concept: A capacitor consists of two separated conductors, usually called plates, We will start with a capacitor consisting of two parallel conducting plates, each with area A separated by a distance d. We assume that these plates are in vacuum (air is very close to a vacuum).

6 Parallel Plate Capacitor Remember the definition of capacitance q Ed q q d 0A A d 0 C V 0 C A d q C qd A 0 C so the capacitance of a parallel plate capacitor is The voltage of a charged capacitor as function of the distance between the plates q V

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9 2. Capacitor Charging (Pengisian Kapasitor) RC Circuits So far we have dealt with circuits containing sources of V and resistors. S R V C Consider a circuit with a source of V, a resistor R, a capacitor C

10 Going around the circuit we can write q dq q V 0 ir 0 V 0 R 0 C dt C dq 1 V 0 q dt RC R The solution of this differential equation is t q ABe RC A and B are constants which we determine from the initial conditions: At t = 0, q = 0, from which we learn that 0=A+B, so B = -A, and at t = Vc = q/c = so we must have q = C = A + 0, thus A = C. The solution for a charging capacitor is thus: = RC (time constant) Tetapan waktu q V 0C 1e t RC

11 A charging capacitor thus has a time dependent charge on it that follows the equation: qt V 0C 1e t RC The voltage across the capacitor is just V(t) = q/c, which gives: To get the time dependent current we differentiate q(t), which gives: V t V 0 1e t RC i t V 0 R e t RC

12 V t V 0 1e t RC t Penentuan kapasitansi dengan waktu paruh 1 untuk V t e RC e t RC ln 2 t RC C t R 1 2 ln 2

13 3. Capacitor Discharging (Pengosongan Kapasitor) V S R ir V C ir q C 0 R dq dt q C 0 The solution of this differential equation is q q 0 e t RC Differentiating charge we get the current i dq dt q 0 RC e t RC C Dalam kondisi saklar terbuka, ujung R langsung dihubungkan dengan C

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15 4. RC Integrator (Pengintergral RC pasif) V in - V c = IR I = C (dv/dt) Take V Vc = Vo we see that if Vo << Vin then the solution to our RC circuit becomes Vo is Integral of Vi

16 Vin +Vp -Vp T/2 t Tegangan masukan (square wave) Untuk = RC << T kapasitor terisi penuh dalam waktu T/2 Vo +Vp t -Vp T Untuk = RC >> T, sebelum kapasitor terisi penuh Vin sudah berubah jadi negatif, akibatnya kapasitor segera dikosongkan. Belum sempat kosong Vin sudah berbalik lagi Vo +Vp -Vp t Vo adalah Integral dari Vin

17 5. RC Differentiator (Diferensiator RC pasif) V R = Vo = I.R Vin = Vc + Vo Vo IR RC dvc dt Vin = Vc + Vo

18 In the limit Vin >> Vout, we have a dierentiator: Vin +Vp -Vp T/2 t Untuk = RC >> T atau f >> 1/RC, Vo mirip dengan masukan, tapi puncak miring Untuk = RC << T atau f << 1/RC, Vo berbentuk denyut dengan Vo = 2Vp Vo +Vp Vo +2Vp +Vp t t -Vp T -Vp -2Vp