Rangkaian Pengisian dan Pengosongan

Kapasitor dan Pengubah Gelombang

Lecture #3

Charging / Discharging of

Capacitor and Wave Converter

Basic electronic / Yohandri

Contents :

Capacitor (review)

Capacitor Charging (Pengisian Kapasitor)

Capacitor Discharging (pengosongan Kapasitor)

RC Integrator (Rangkaian Pengintergral RC pasif )

RC Differentiator (Rangkaian Pendifferensial RC pasif)

Basic electronic / Yohandri

Menganalisis rangkaian pengisian dan

pengosongan kapasitor dan

penerapannya pada kehidupan

Menganalisis rangkaian pengintergral RC

pasif (Integrator) dan rangkaian

pendifferensial RC pasif (Differensiator)

Kompetensi Dasar

Basic electronic / Yohandri

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.

Basic electronic / Yohandri

• 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).

Basic electronic / Yohandri

Parallel Plate

Capacitor

V

qC

d

A

dA

q

q

Ed

qC 0

0

d

AC 0

A

qd

C

qV

0

The voltage of a charged capacitor as function of the

distance between the plates

Remember the definition of capacitance

so the capacitance of a parallel plate capacitor is

Basic electronic / Yohandri

Basic electronic / Yohandri

Basic electronic / Yohandri

2. Capacitor Charging (Pengisian Kapasitor)

RC Circuits

R

CV

S

So far we have dealt with circuits containing

sources of V and resistors.

Consider a circuit with

a source of V,

a resistor R,

a capacitor C

Basic electronic / Yohandri

Going around the circuit we can write

tRCq A Be

The solution of this differential equation is

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:

0 0

0

0 0

1

q dq qV iR V R

C dt C

Vdqq

dt RC R

0 1

tRCq V C e

= RC (time constant) Tetapan waktu

Basic electronic / Yohandri

A charging capacitor thus has a

time dependent charge on it

that follows the equation:

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:

0 1tRCq t V C e

0

tRC

Vi t e

R

0 1tRCV t V e

Basic electronic / Yohandri

0 1tRCV t V e

Penentuan kapasitansi

dengan waktu paruh

2

1

21 Vuntukt

RC

t

e12

RCt

e

2

1

RCt 2ln

2ln

21

R

tC

Basic electronic / Yohandri

3. Capacitor Discharging (Pengosongan Kapasitor)

R

CV

S

Dalam kondisi saklar

terbuka, ujung R

langsung dihubungkan

dengan C

iR VC iR q

C 0 R

dq

dtq

C 0

q q0et

RC

i dq

dt

q0

RC

e

t

RC

The solution of this differential equation is

Differentiating charge we get the current

Basic electronic / Yohandri

Basic electronic / Yohandri

4. RC Integrator (Pengintergral RC pasif)

Vin - Vc= 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

Basic electronic / Yohandri

t

Vin

+Vp

-Vp

T/2

t

Vo

+Vp

-Vp

T

t

+Vp

-Vp

Vo

Untuk = RC << T kapasitor terisi penuh dalam waktu T/2

Untuk = RC >> T, sebelum kapasitor terisi penuh Vin sudah

berubah jadi negatif, akibatnya kapasitor segera dikosongkan.

Belum sempat kosong Vin sudah berbalik lagi

Tegangan masukan (square wave)

Vo adalah Integral dari Vin

5. RC Differentiator (Diferensiator RC pasif)

Vin = Vc + Vo

VR = Vo = I.R

dt

dVcRCIRVo

Vin = Vc + Vo

Basic electronic / Yohandri

In the limit Vin >> Vout, we have a dierentiator:

t

Vin

+Vp

-Vp

T/2

t

Vo

+Vp

-Vp

T

t

Vo

+Vp

-Vp

+2Vp

-2Vp

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

Basic electronic / Yohandri