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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