lecture #3 - andipiliang.files.wordpress.com · rangkaian pengisian dan pengosongan kapasitor dan...
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Rangkaian Pengisian dan Pengosongan
Kapasitor dan Pengubah Gelombang
Lecture #3
Charging / Discharging of
Capacitor and Wave Converter
Basic electronic / Yohandri
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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
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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
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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
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• 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
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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
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Basic electronic / Yohandri
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Basic electronic / Yohandri
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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
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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
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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
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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
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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
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Basic electronic / Yohandri
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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
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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
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5. RC Differentiator (Diferensiator RC pasif)
Vin = Vc + Vo
VR = Vo = I.R
dt
dVcRCIRVo
Vin = Vc + Vo
Basic electronic / Yohandri
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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