THEORY AND DESIGN OF ELECTRONIC CIRCUITS
E. TAIT
FOR ELEKTRODA PEOPLE

Theory and Design of

Electrical and Electronic CircuitsIndex

Introduction

Chap. 01 Generalities

Chap. 02 Polarization of components

Chap. 03 Dissipator of heat

Chap. 04 Inductors of small value

Chap. 05 Transformers of small value

Chap. 06 Inductors and Transformers of great value

Chap. 07 Power supply without stabilizing

Chap. 08 Power supply stabilized

Chap. 09 Amplification of Audiofrecuency in low level class A


Chap. 25 Amplitude Modulation

Chap. 26 Demodulación of Amplitude

Chap. 27 Modulation of Angle

Chap. 28 Demodulation of Angle

Chap. 29 Heterodyne receivers

Chap. 30 Lines of Transmission

Chap. 31 Antennas and Propagation

Chap. 32 Electric and Electromechanical installations

Chap. 33 Control of Power (I Part)

Chap. 34 Control of Power (II Part)

Chap. 35 Introduction to the Theory of the Control

Chap. 36 Discreet and Retained signals

Chap. 37 Variables of State in a System

Chap. 38 Stability in Systems

Chap. 39 Feedback of the State in a System


Introduction
System of units
Algebraic and graphical simbology
Nomenclature
Advice for the designer

_______________________________________________________________________________Introduction

In this chapter generalizations of the work are explained.
Almost all the designs that appear have been experienced satisfactorily by who speaks to them.
But by the writing the equations can have some small errors that will be perfected with time.
The reading of the chapters must be ascending, because they will be occurred the subjects
being based on the previous ones.

System of units

Except the opposite clarifies itself, all the units are in M. K. S. They are the Volt, Ampere,
Ohm, Siemens, Newton, Kilogram, Second, Meter, Weber, Gaussian, etc.
The temperature preferably will treat it in degrees Celsius, or in Kelvin.
All the designs do not have units because incorporating each variable in M. K. S., will be
satisfactory its result.

Algebraic and graphical simbology

Often, to simplify, we will use certain symbols. For example:



or v
p
— maximum V
max
— permissible (limit to the breakage) V
ADM

Advice for the designerAll the designs that become are not for arming them and that works in their beginning, but to only
have an approximated idea of the components to use. To remember here one of the laws of
Murphy: " If you make something and works, it is that it has omitted something by stop ".
The calculations have so much the heuristic form (test and error) like algoritmic (equations)
and, therefore, they will be only contingent; that is to say, that one must correct them until reaching
the finished result.
So that a component, signal or another thing is despicable front to another one, to choose among
them 10 times often is not sufficient. One advises at least 30 times as far as possible. But two
cases exist that are possible; and more still, up to 5 times, that is when he is geometric (5
2
= 25),
that is to say, when the leg of a triangle rectangle respect to the other is of that greater magnitude
or. This is when we must simplify a component reactive of another pasive, or to move away to us of
pole or zero of a transference.
As far as simple constants of time, it is to say in those transferences of a single pole and that is
excited with steps being exponential a their exit, normally 5 constants are taken from time to arrive
in the end. But, in truth, this is unreal and little practical. One arrives at 98% just by 3 constants
from time and this magnitude will be sufficient.
As far as the calculations of the permissible regimes, adopted or calculated, always he is advisable


Bipolar transistor of junction (TBJ)

Theory

Polarizing to the bases-emitter diode in direct and collector-bases on inverse, we have the
model approximated for continuous. The static gains of current in common emitter and common
bases are defined respectively β = h
21E
= h
FE
= I
C
/ I
B
~ h
21e
= h
fe
(>> 1 para TBJ comunes)
α = h
21B
= h
FB
= I
C
/ I

T
= 0,000172 . ( T + 273 )
I
CB
= I
CB0(25ºC)
. 2
∆T/10

with ∆T the temperature jump respect to the atmosphere 25 [ºC]. From this it is then

∆T = T - 25

∂I
CB
/ ∂T = ∂I
CB
/ ∂∆T ~ 0,07. I
CB0(25ºC)
. 2
∆T/10

On the other hand, the dependency of the bases-emitter voltage respect to the temperature, to
current of constant bases, we know that it is

∂V
BE
/ ∂T ~ - 0,002 [V/ºC]

The existing relation between the previous current of collector and gains will be determined now

BE
+ I
CB
)
β = α / ( 1 - α )
α = β / ( 1 + β )

Next let us study the behavior of the collector current respect to the temperature and the
voltages

∆I
C
= (∂I
C
/∂I
CB
) ∆I
CB
+ (∂I
C
/∂V
BE
) ∆V
BE
+ (∂I
C
/∂V
CC
) ∆V
CC

- V
EE
= I
B
(R
BB
+ R
EE
) + V
BE
+ I
C
R
EE
I
C
= [ V
BB
- V
EE
- V
BE
+ I
B
(R
BB
+ R
EE
) ] / [ R
E

) = (∂I
C
/∂V
EE
) = - (∂I
C
/∂V
BB
) = - 1 / ( R
E
+ R
BB
β
-1
)
(∂I
C
/∂V
CC
) = 0

being

∆I
C
= [ 0,07. 2
∆T/10
(R
BB
+ R

(∆V
BB
- ∆V
EE
)

Design

Be the data

I
C
= ... V
CE
= ... ∆T = ... I
Cmax
= ... R
C
= ... From manual or the experimentation according to the graphs they are obtained

β = ... I
CB0(25ºC)
= ... V
BE
= ... ( ~ 0,6 [V] para TBJ de baja potencia)
. R
BB
/ R
S
= 0
∆V
EE
= 0
R
EE
= R
E
R
CC
= R
C

and if to simplify calculations we do

R
E
>> R
BB
/ β

us it gives

S
I
= 1 + R

E
= ... >> 0,002 . ∆T / ∆I
Cmax
R
E
[ ( ∆I
Cmax
/ 0,07. 2
∆T/10
I
CB0(25ºC)
. ∆T ) - 1 ] = ... > R
BB
= ... << β R
E
= ...

being able to take a ∆I
C
smaller than ∆I
Cmax
if it is desired.
Next, as it is understood that

V
BB
= I
B
R
BB

E
R
E
~ I
C
( R
C
+ R
E
) + V
CE
= ...

they are finally

R
B
= R
BB
V
CC
/ V
BB
= ...
R
S
= R
B
R
BB

E
> 500 [Ω] that they are generally sufficient in all thermal stabilization.
Be the data

I
C
= ... V
CE
= ... R
C
= ...

From manual or the experimentation they are obtained

β = ...

what will allow to adopt with it

I
S
= ... >> I
C
β
-1
V
R
E

S
= ...
R
B
= ( V
CC
- 0,6 - V
R
E
) / I
S
= ...

Unipolar transistor of junction (JFET)

Theory

We raised the equivalent circuit for an inverse polarization between gate and drain, being I
G

the current of lost of the diode that is

I
G
= I
G0
(1 - e
V
Gs
/V


I
D
~ I
DSS
[ 2 V
DS
( 1 + V
GS
/ V
P
) / V
P
- ( V
GS
/ V
P
)
2
] con V
DS
< V
P
I
D
~ I
DSS
( 1 + V
GS
/ V

/∂V
DD
) ∆V
DD
+ (∂I
D
/∂V
SS
) ∆V
SS
+ (∂I
D
/∂V
GG
) ∆V
GG
+

+ (∂I
D
/∂i
G
) ∆I
G
+ (∂I
D
/∂V
GS
) ∆V
GS

) / R
SS
∂I
D
/∂V
GG
= - ∂I
D
/∂V
SS
= 1 / R
SS
∂I
D
/∂T = (∂I
D
/∂V
GS
) (∂V
GS
/∂T) + (∂I
D
/∂I
G
) (∂I
G
/∂T) =
= ( -1/R
SS
) ( 0,00012 ) + ( 0,7.I

I
D
= ... V
DS
= ... ∆T = ... ∆I
Dmax
= ... R
D
= ... From manual or the experimentation according to the graphs they are obtained

I
DSS
= ... I
GB0(25ºC)
= ... V
P
= ... and therefore

R
S
= V
P
[ 1 - ( I
D

Operational Amplifier of Voltage (AOV)

Theory

Thus it is called by its multiple possibilities of analogical operations, differential to TBJ or JFET
can be implemented with entrance, as also all manufacturer respects the following properties:

Power supply (2.V
CC
) between 18 y 36 [V]
Resistance of input differential (R
D
) greater than 100 [KΩ]
Resistance of input of common way (R
C
) greater than 1 [MΩ]
Resistance of output of common way (R
O
) minor of 200 [Ω]
Gain differential with output in common way (A
0
) greater than 1000 [veces]

We can nowadays suppose the following values: R
D
= R
C
=
∞
, R

OS
with respect to temperature α
T
and to the voltage of feeding α
V
.
If we added all these defects in a typical implementation

R
C
= V
1
/ I
B
V
1
= V
O
. (R
1
// R
C
) / [ R
2
+ (R
1
// R
C
) ]


)

arriving finally at the following general expression for all offset

V
O
= V
OS
( 1 + R
2
/ R
1
) + I
OS
R
3
( 1 + R
2
/ R
1
) + I
B
[ R
2
- R
3
( 1 + R
2
/ R
1

1
)

and for the one of TBJ that is designed with R
3
= R
1
// R
2

V
O
= ( V
OS
+ I
OS
R
3
+ α
T
∆T + α
T
∆V
CC
)

( 1 + R
2
/ R
1

= ... V
CC
= ... A = ... P
AOVmax
= ... (normally 0,25 [W]) With the previous considerations we found

R
3
= ... >> V
CC
/ ( 2 I
B
- I
OS
)
R
1
= ( 1 + 1 / A ) R
3
= ...
R
2
= A R
1
= ...
R
L

/ 0,25 < R
B
= ... << R
N
2 R
A
= ( 2 V
CC
- V
R
B
) / ( V
R
B
/ R
B
)
⇒
R
A
= R
B
[ ( V
CC
/ V
R
B
) - 0,5 ] = ...

_________________________________________________________________________________

= T
-1
.
∫
0
T
p
∂
t = T
-1
.
∫
0
T
i.v
∂
t

and it can be actually of analytical or geometric way.
Also, this constant P, can be thought as it shows the following figure in intervals of duration
T
0
, and that will be obtained from the following expression

T
0
= P
0
/ P


the ambient temperature. For the worse case

p
ADM
= P
ADM
θ
JC
/

Z
JC

= P
ADM
. M

being M a factor that the manufacturer specifies sometimes according to the following graph
Continuous regime

When the power is not repetitive, the equations are simplified then the following thing

P
ADM
= ( T
JADM
- T

+ θ
DA
θ
CA
= ( T
C
- T
A
) / P
MAX
= ( T
C
- T
A
) ( T
JADM
- T
A
) / P
ADM
( T
JADM
- T
C
)Design

Be the data

dissipator

T
J
= ... < T
JADM

and with it (it can be considered θ
DA

~
1 [ºC/W] )

θ
DA
= θ
CA
- θ
DA
= { [ ( T
J
- T
A
) / P ] - θ
JC
} - 1 = ...

and with the aid of the abacus following or other, to acquire the dimensions of the dissipator
.ω
2
, not deigning the one that of losses of heat by the ferromagnetic nucleus;
capacitance C will be it by addition of the loops; and finally inductance L by geometry and nucleus.
This assembly will determine an inductor in the rank of frequencies until ω
0
given by effective
the L
ef
and R
ef
until certain frequency of elf-oscillation ω
0
and where one will behave like a
condenser.

The graphs say

Z = ( R + sL ) // ( 1 / sC ) = R
ef
+ s L
ef
R
ef
= R / [ ( 1 - γ )
2
+ ( ωRC)
2
]
~

= ωL
ef
/ R
ef
= Q ( 1 - γ )

Q- meter

In order to measure the components of the inductor the use of the Q-meter is common. This
factor of reactive merit is the relation between the powers reactive and activates of the device, and for
syntonies series or parallel its magnitude agrees with the overcurrent or overvoltage, respectively, in
its resistive component.
In the following figure is its basic implementation where the Vg amplitude is always the same
one for any frequency, and where also the frequency will be able to be read, to the capacitance
pattern C
P
and the factor of effective merit Q
ef
(obtained of the overvalue by the voltage ratio between
the one of capacitor C
P
and the one of the generator v
g
). The measurement method is based on which generally the measured Q
ef
to one ω
ef

= V
g
( R + sL ) / ( R + sL ) // ( 1/sC ) = K ( s
2
+ s. 2 ξ ω
0
+ ω
0
2
)
K = V
g
L C
ω
0
= ( LC )
-1/2
ξ = R / 2 ( L / C )
1/2that not to affect the calculations one will be due to work far from the capacitiva zone (or resonant), it
is to say with the condition

ω << ω
0

then, varying ω and C
P
we arrived at a resonance anyone detecting a maximum V

p2
= ...
Q
ef2max
=
...

we will be able then to find

C = ( n
2
C
p2
- C
p1
) ( 1 - n
2
)
-1
=
...
L = [ ω
ef1
2

( C + C
p1
) ]
-1
=

= ω
ef1
L
ef1
/ Q
ef1max
=
...
R
ef2
= ω
ef2
L
ef2
/ Q
ef2max
=
...

and as it is

R = R
CC
+ ρ
CA
ω
2
=

R

L C

)
2
] / ω
ef1
2
( 1 - n
2
) =
...
R
CC
= R
ef1
( 1 - ω
ef1
2

L C

)
2
- ρ
CA
ω
ef1
2

=