Full text
Purpose
To be armed with appropriate means
and working instruments to understand
the operating principle of the electronic
devices and their applications.
On-line circuit simulator
 One can simulate the existing circuits (selected
from "Circuits" menu) or new circuits created by
the user ("Circuits/Blank Circuit" menu). New
circuits are automatically saved; to access them
later, their link should be exported ("File/Export
Link")
 http://www.falstad.com/circuit/e-index.html
 It is possible to download the application on a
workstation and simulate off-line.
Content
Basic knowledge for every explorer in the
electronics domain:
 electrical signals
 laws, theorems, formulas used in electric circuits
 voltage and current sources
 passive components
 RC circuits - behavior in the time and frequency
domains
Electrical signals
VI [V]
vi [V]
Time variation of a:
a) continous voltage (dc);
b) sinusoidal voltage (ac)
Sources.
Notations
Formulas, laws and theorems
of electric circuits
 Ohm’s laws
 Kirchhoff’s laws (KCL and KVL)
 Resistors connection
 Resistive dividers
 Superposition effect method
V0 = V01+V02
 Thevenin’s theorem
(equivalent voltage generator)
 Millman’s theorem (nodes potential theorem)
M - the reference point
 Power. Power transfer
PS=VSI=10V·(-5mA)=-50mW; the power is generated by the source.
PR=VRI’=10V·5mA=50mW; the power is dissipated by the resistor.
Capacitor and inductor
Current - voltage relation
Series and parallel connection
Time domain behavior
Frequency domain behavior
C in the time domain
C
Defining relation between
current and voltage
iC
vC
CdvC (t )  iC (t )dt
Considering finite variations:
CvC  iC t
RC circuit – time domain analyses
 RC circuit with a dc voltage source
RiC (t )  vC t   vI t 
CdvC (t )  iC (t )dt
dvC (t )
iC (t )  C
dt
vI
dvC t 
RC
 vC t   vI t 
dt
  RC
t
time constant of the circuit
t
vC (t )  vC (0)e   (1  e  )vC ()
RC circuit with a dc voltage source
t
t
vC (t )  vC (0)e   (1  e  )vC ()
vC ()
vC (0)
vC (t )
Example
R=5kΩ, C=100nF.
At the initial time moment the capacitor has 0V voltage drop. The input
voltage is VI1=9V for the first 5ms, then it becomes VI2=-5V for the
next 1ms.
a) How does the time variations (waveforms) of the voltage and
current for the capacitor look like?
b) What are the final values of the voltage and current for the
capacitor?
c) What would be the final values ​of current and voltage for the
capacitor if the capacitor would have the value C=22nF?
on-line simulation
 RC circuit with rectangular voltage source
Results
obtained by
simulation
t
t
vO (t )  vO (0)e   (1  e  )vO ()
vO (t )  ?
T
T
5  ;  
2
10
T
 5
2
19 / 21
  T
Compute the average value of the input voltage
A
B
A
B
20 / 21
 Charging up a C with a constant current
Cdvc t   ic t dt
t
1
vC (t )   iC (t )dt  vC (0)
C0
1
vC (t )  It  vC (0)
C
 Reactive components in ac regim (frequency domain)
2
  2f 
T
Reactance
Impedance
1
XC 
; for capacitor
C
X L  L; for inductor
Z  R  jX L  X C 
ZC  R  jX C ;
Impedance of
ideal reactive
elements
1
ZC 
;
jC
Z L  R  jX L
Z L  jL
What are the equivalent of C and L in dc
(after the transient regime ?)
RC circuit - frequency response
Passive
low-pass
filter
(LPF)
Transfer function
vO ( j )
1
F ( j ) 

vI ( j ) 1  jRC
F ( j ) 
1
1  (RC )
2
()  arctg(RC)
Frequency Response Representation
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