- 120 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Capacitors' - morrison

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Illustrated applications of capacitors

- Power supply decoupling:

See capacitor C1

- Signal decoupling:

See capacitor C2

- Signal coupling:

See capacitors C3 and C4

Some other applicationsof capacitors

- RC Filters: See later
- Tuned circuits: In another talk

(We need to discuss inductors first)

Fields

- Electric fields
- Capacitors
- Magnetic Fields
- Inductors
- Electromagnetic (EM) fields
- Radio waves
- Antennas
- Cables

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

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 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

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.

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

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 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).

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

Download Presentation

Connecting to Server..