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Capacitors. BITX20 bidirectional SSB transceiver. A BITX20 single stage. A simplified single stage. A simplified single stage with capacitors. C4. C3. C2. C1. Illustrated applications of capacitors. Power supply decoupling : See capacitor C1 Signal decoupling : See capacitor C2

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Capacitors

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Capacitors l.jpg

Capacitors


Slide2 l.jpg

BITX20 bidirectional SSB transceiver


A bitx20 single stage l.jpg

A BITX20 single stage


Slide4 l.jpg

A simplified single stage


Slide5 l.jpg

A simplified single stage with capacitors

C4

C3

C2

C1


Illustrated applications of capacitors l.jpg

Illustrated applications of capacitors

  • Power supply decoupling:

    See capacitor C1

  • Signal decoupling:

    See capacitor C2

  • Signal coupling:

    See capacitors C3 and C4


Some other applications of capacitors l.jpg

Some other applicationsof capacitors

  • RC Filters: See later

  • Tuned circuits: In another talk

    (We need to discuss inductors first)


Fields l.jpg

Fields

  • Electric fields

    • Capacitors

  • Magnetic Fields

    • Inductors

  • Electromagnetic (EM) fields

    • Radio waves

    • Antennas

    • Cables


Capacitors9 l.jpg

Capacitors


Discharge of a capacitor l.jpg

Discharge of a capacitor


Graph of capacitor discharge from 10v r 1 ohm c 1 farad or r 1 m ohm c 1 uf l.jpg

Graph of capacitor discharge from 10VR=1 Ohm, C=1 Farad (or R=1 M Ohm, C=1 uF)


The same discharge from 27 18v l.jpg

The same discharge from 27.18V

e=2.718

10*2.718

10

10/2.718


Exponential decay l.jpg

Exponential decay

The RC decay time constant = R times C

If R is in Ohms and C in farads the time is in seconds

Every time constant the voltage decays by the ratio of 2.718

This keeps on happening (till its lost in the noise)

This ratio 2.718is called “e”.


Exponential decay14 l.jpg

Exponential decay

It’s a smooth curve. We can work out the voltage at any moment.

The voltage at any time t is: V = V0 / e(t/RC)

V0 is the voltage at time zero.

t/RC is the fractional number of decay time constants

For e( ) you can use the ex key on your calculator


Low pass rc filter l.jpg

Low pass RC filter


Rc 1 second vin 10v square wave l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave17 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave18 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave19 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave20 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave21 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave22 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v square wave23 l.jpg

RC = 1 secondVin = +/-10V square wave


Rc 1 second vin 10v sine wave l.jpg

RC = 1 secondVin = +/-10V sine wave


Rc 1 second vin 10v sine wave25 l.jpg

RC = 1 secondVin = +/-10V sine wave


Rc 1 second vin 10v sine wave26 l.jpg

RC = 1 secondVin = +/-10V sine wave


Rc 1 second vin 10v sine wave27 l.jpg

RC = 1 secondVin = +/-10V sine wave


Rc 1 second vin 10v sine wave28 l.jpg

RC = 1 secondVin = +/-10V sine wave


Rc 1 second vin 10v sine wave29 l.jpg

RC = 1 secondVin = +/-10V sine wave


Rc 1 second vin 10v sine wave30 l.jpg

RC = 1 secondVin = +/-10V sine wave


What can we say about the phase l.jpg

What can we say about the phase?

The voltage across a resistor is always in phase with the current through it

The voltage across a capacitor lags the current through it by 90 degrees

So in an RC series circuit the phases of the R and C voltages are 90 degrees different.


Our low pass rc filter l.jpg

Our low pass RC filter


What can we say about the amplitude l.jpg

What can we say about the amplitude?

The higher the frequency the more current is needed to charge and discharge a capacitor to the same voltage.

(Ignoring phase) we could say it has less resistance the higher the frequency. This is what we call impedance.

The impedance of a capacitor in Ohms is 1/(2Pi*f*C)

Where f is the frequency in Hertz and C the capacitance in Farads.

(2Pi*f is also known as the frequency in radians per second w)


Vector diagram for the low pass filter l.jpg

Vector diagram for the low pass Filter

Leading Lagging

So Vout lags (Vin-Vout) by 90 degrees.

So we can calculate the filter output using Pythagoras

As the frequency increases Vout moves round the circle from the top to the bottom on the right


Vector diagram for the low pass filter35 l.jpg

Vector diagram for the low pass Filter

Leading Lagging

This diagram shows the corner frequency of the filter.

This is the 3dB down point and the phase lag is 45 degrees

This happens when the impedance of R and C are the same.

R = 1/(2Pi*f*C).


Low pass gain against frequency l.jpg

Low pass gain against frequency

0.707


Low pass phase against frequency l.jpg

Low pass phase against frequency

-45


High pass rc filter l.jpg

High pass RC filter


Vector diagram for the high pass filter l.jpg

Vector diagram for the high pass Filter

Leading Lagging

So Vout leads (Vin-Vout) by 90 degrees.

So we can calculate the filter output using Pythagoras

As the frequency increases Vout moves round the circle from the bottom to the topon the left


Slide40 l.jpg

Our simplified single stage with capacitors

C4

C3

C2

C1


Questions l.jpg

Questions?


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