Lecture #3 Charging / Discharging of Capacitor and Wave Converter Rangkaian Pengisian dan Pengosongan Kapasitor dan Pengubah Gelombang
Contents : Capacitor (review) Capacitor Charging (Pengisian Kapasitor) Capacitor Discharging (pengosongan Kapasitor) RC Integrator (Rangkaian Pengintergral RC pasif ) RC Differentiator (Rangkaian Pendifferensial RC pasif)
Kompetensi Dasar Menganalisis rangkaian pengisian dan pengosongan kapasitor dan penerapannya pada kehidupan Menganalisis rangkaian pengintergral RC pasif (Integrator) dan rangkaian pendifferensial RC pasif (Differensiator)
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.
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).
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
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
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
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
V t V 0 1e t RC t Penentuan kapasitansi dengan waktu paruh 1 untuk V 2 1 2 t e RC 1 2 1 2 e t RC ln 2 t RC C t R 1 2 ln 2
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
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
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
5. RC Differentiator (Diferensiator RC pasif) V R = Vo = I.R Vin = Vc + Vo Vo IR RC dvc dt Vin = Vc + Vo
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