1/39 passive components and circuits - ccp lecture 11
TRANSCRIPT
1/39
Passive components and circuits - CCP
Lecture 11
2/39
Content
Passive components with variable parameters Variable resistors Variable capacitors Adjustable coils
Passive components with special construction Passing capacitors (condensatoare de trecere) Capacitors with commanded capacitance (diode varicap) Embedded capacitors Embedded coils
3/39
Variable resistors
Generically called potentiometers, they are divided in two categories:
Semi adjustable resistors
Adjustable resistors (potentiometers )
4/39
Variable resistors - usage
Potentiometer connection
Rheostat connection
Ip
IO vRR
Rv
RRR
Rv
2
21
2
x
IO RR
vi
v I
vO
RR1
R2
Rp
v I iO
R
Rp
Rx
5/39
Variable resistors - clasification
According to the manufacturing of the resistive element: With metallic coat (pellicle) With carbon coat With metal ceramic coat (cermet) Reeled
6/39
Circular reeled potentiometer
7/39
Variable resistors - clasification
According to the number of resistive elements: Simple, with a single
resistive element;
Multiple, together or independently drive;
8/39
Variable resistors - clasification
According to their destination: For mass
consumption; For precision (with
smaller tolerances and higher reliability);
According to the to the variation of the resistance depending on the position of the cursor: Liniar Logarithmic Invers logarithmic Exponential Invers exponential S type
9/39
Variable resistors - parameters They are characterized by the same parameters as the
fixed resistors. The tolerance for the potentiometers do not usually have
very small values, considering the fact that the positioning of the cursor can not be made with a very high precision. In order to obtain a high resolution in positioning the cursor the multi-tour potentiometers are manufactured.
10/39
Variable resistors – specific parameters
The residual resistance, r0 – represents the value of the resistance measured between the cursor and one of the ends when the cursor is found on that end. Ideally, this parameter should be null.
The contact resistance, rk – represints the resistance between the mobile contact and the resistive element. This parameter should also be as small as possible.
The limit cursor current, In – is the maximum current that can flow through the resistive element.
11/39
Variable resistors – specific parameters The resistance’s
law of variation: Liniar
Logarithmic
Invers logarithmic
nRrR 0
0
ln
0r
Rn
erR
0
ln
0 1 r
R
n
n
eRrR
12/39
Variable resistors - mechanical parameters Mechanic endurance – the minimum number of
actions during which the potentiometer should keep its electric characteristics constant. This parameter takes values between 10.000 and 25.000 for actual potentiometers and 100-200 for semi-adjustable.
The pressing force – represents the force with which the cursor pushes over the resistive coat (pellicle).
13/39
Variable capacitors with dielectric air They consist of a succession of plates,
some fixed-stators and others mobile-rotors. The plates of the rotor interpenetrate with the ones of the stator. When rotating the superposed surface of the places is smaller or larger, in this way modifying the capacitance.
Unlike the potentiometers, variable capacitors have only two terminals. Therefore they can be used only in assemblies equivalent to the rheostat assembly.
They are used in filters for which selectivity must be modified during functioning.
14/39
Variable capacitors – parameters Parameters with the same meanings as in
fixed capacitors: Nominal capacity (referring to the maximum value
of the capacitance); The tolerance of the nominal capacity; Tangent of the loss angle; The isolation resistance; The breakout voltage ; The temperature coeficient .
15/39
Specific parameters: The actual rotation angle; The residual capacitance; The maximum variation of capacitance (Cn-Crez); The variation law of the capacitance:
The reversibility; The rotation momentum of the mobile plate
, , ; α rotation anglen rezC f C C
Variable capacitors – parameters
16/39
Adjustable capacitors
They are also called trimmers, being the equivalent of the semi adjustable resistors.
Their capacitance is modified when starting to function or during the periodic adjustment of the equipment.
According to the nature of the dielectric they can be with air, ceramics, or with organic dielectric.
The values of the capacitances are very small (of pF order).
17/39
Adjustable coils
The value of the inductance is adjusted by inserting the ferrite core in the body of the coil.
18/39
Special capacitors – passing capacitors These capacitors are used when
signals are passing through the walls of the electromagnetic screens (metallic walls).
They are manufactured with ceramic dielectrics of type II that allow the obtaining of high specific capacitances. A plate is manufactured inside the ceramics, and the other one is obtained in the exterior by metallization. This will be stuck to the wall of the screen.
19/39
Special capacitors – nonliniar (varicap diodes) Their capacitance is variable
according to the continuous voltage applied on the terminals.
They are used in selective filtering circuits. The mechanical command (from the adjustable capacitors) is replaced with an electrical command, the continuous voltage applied.
They are polarized capacitors (they involve a total voltage to be applied, voltage that keeps the diode blocked)
20/39
Special capacitors – printed (embedded) They are obtained directly on the
interconnecting structures (electronic boards, multichip modules, etc.) by manufacturing the plates on each of the two sides of the isolating layer used or by manufacturing some “comb” structures on the same side (in order to increase the surface of the plates).
The dielectric between the two plates is the sub-layer of the board or this together with the air.
The values obtained for capacitances are small.
21/39
Capacitance between two parallel tracks - case I
F/m0
pF/m
0,225 pF/in
8,84
wC Kr Cl d
wKr C d
wKr C d
If d/w<<1, then KC=1
t
lw
substratizolator
d
r
22/39
Fringing factor KC
0
0
2
1
4
2
6
3
8
4
10
5
12
6
14
7
16
8
18
9
20
10K C
d/w
5,4r+V
-V linii de flux ideale
linii de flux reale
suprafaţă de
potenţial nul
23/39
Capacitance between two parallel tracks - case II
0 ( )
( )
( )
F/m( )
ln 1
27,8pF/m
( )ln 1
0,71pF/in
( )ln 1
r eff
r eff
r eff
Cl d w
w t
d ww t
d ww t
l
d
t
w
substratizolator r
24/39
Equivalent relative permittivity
The electric relative permitivity is the result of placing the conductors in a non-homogeneous dielectric medium. The value of the parameter is calculated is calculated according to the relative permeability of the sub-layer and the geometric dimensions of the capacitors:
0,5 2
0,5
1 1 121 0,04 1 for
2 2
1 1 121 for
2 2
r rreff
r rreff
h ww h
w h
hw h
w
25/39
Capacitance between two parallel tracks - case II (particular situations)
0 ( )
( )
( )
F/mln
27,8pF/m
ln
0,71pF/in
ln
r eff
r eff
r eff
Cl d
w t
dw t
dw t
0 ( )
2 2
( )
2 2
( )
2 2
2F/m
1 1ln
1 2
55,6pF/m
1 1ln
1 2
1,41pF/in
1 1ln
1 2
r eff
r eff
r eff
Cl
dw t w t
dw t w t
dw t w t
If d>>w: If the tracks have different widths:
26/39
Capacitance of a track placed over a ground plane
0 F/m
8,83 pF/m 0,225 pF/in
r C
r C r C
wC Kl h
w wK K
h h
substratizolator
l
t
w
h
plan demasã
r
0
0
2
1
4
2
6
3
8
4
10
5
12
6
14
7
16
8
18
9
20
10K C
2h/w
5,4r
27/39
Capacitance between two tracks placed over a ground plane
20
2 2
For 2 / 0,3
F/m
2,81 pF/m 0,07 pF/in
rL C
r L C r L C
h d
wC K Kl d
w wK K K K
d d
0
0
2
1
4
2
6
3
8
4
10
5
12
6
14
7
16
8
18
9
20
10
0
2
4
6
8
10
12
14
16
18
20
K C
d/w
5,4r
K L
K L
K Cl
d
tw
substratizolator r
plan demasã
h
28/39
Special coils – printed (embedded) Sometimes, when small inductances are required, one
can manufacture them directly on the electronic module (board, multi-chip module, semiconductor) resulting embeded coils.
The formulas presented below can be used for dimensioning such coils.
29/39
Inductance between two parallel tracks with rectangular section - A
H1tw
)wd(ln0rlL
For 1and
0 ln H/m
0, 4 ln μH/m
0, 01 ln μH/in
w t dr
dL r ( )l w t
dL( )
l w t
dL( )
l w t
l
d
i i
spre sarcinã
t
w
substratizolator
30/39
Inductance between two parallel tracks with rectangular section placed on different sides - B
Hw
d
LKr26,1
l
Hw
d
LK0rlL
l
i
i
spre sarcinã
t
w
substratizolator
d
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
20K L
d/w
31/39
Inductance of a track placed over a ground plane
Hw
h
LKr26,1
l
Hw
h
LK0rlL
0
0
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
20
20K L
2h/w
substratizolator
l
i
i
spre sarcinã
t
w
h
plan demasã
32/39
Plane spiral circular inductor
2 2 23,2 10[μH]; where
6 10
[ m] [ m]4 2a i a i
a NL
a cd d d d
a c
33/39
Plane spiral squared inductor
2 20,0122[μH];
4 11where c is track width
l NL
l c
34/39
Annexe Remember the following values :
1 inch=2,54 cm 1 mil (mils)=1 inch/1000 =0,0254 mm 0=8,8542·10-12 F/m
0=4·π·10-7 H/m
Recommended web pages: http://www.megaconverter.com/mega2/ http://scienceworld.wolfram.com/physics/
35/39
Problem 1
The AB connection is made on a double layer PCB, with dielectric with r=4,5, with Copper tracks with
=6,787 x 10-7 -inch, with topology from figure and the following dimensions: length l=2 in, substrate width d=10 mil, track thickness t=5 mil and track width w=20 mil.
Rs
Rl
A B
vOv
I 2 in
100
10K
t
lw
substratizo lator
d
r
36/39
Problem 1 Determine the electrical parameters of connection . Draw the electrical diagram of the circuit, including connection
parameters. Determine the transfer function H(j)=vo(j)/vi(j) Neglecting the inductive effect of connection, how does it
looks the waveform of the output voltage if the vi source applies rectangular pulses with 5ns duration?
Neglecting the capacitive effect of connection, how does it look the waveform of the output voltage if the vi source applies rectangular pulses with 5ns duration?
37/39
Problem 2
A variable capacitor has 13 plates in rotor. The plates shape is semi-circular with 2 cm radius. The axis diameter is 0.8 cm. The distance between the plates is 0.5 mm.
Determine the nominal capacitance. In series with this capacitor is connected a resistor,
marked with 1K2 M. Determines the limits of time constant.
38/39
Problem 3
On a 4 layers PCB, the internal layers are used for ground and power supply, and are made as continuous planes with vias (pass holes). The PCB dimensions are 8 x 10 inch2. In the PCB are made 874 holes, with 50 mil diameter and 4 holes with 0.1 inch diameters. The PCB dielectric has d=10 mil thickness and is characterized by r=4,8.
Determine the equivalent capacitance between the ground and the power supply connections.
How much is the width of the 2 inch length track, positioned over the ground plane in order to have a 20pF capacitance regarding ground?
39/39
Problem 4
On the previous PCB, a spiral squared inductor with 4 turns is realized. The track width is 10 mil and the distance between the tracks is 10 mil. The thickness of the Cu (=6,787 x 10-7 -inch) track is 5 mil.
What’s the value of the obtained inductance? What is the value of the quality factor at the 1KHz
frequency? What is the coil’s capacitance regarding the ground?