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page 64

6.1.1 RMS Values

When dealing with alternating currents we are faced with the problem of how we represent the signal magnitude. One easy way is to use the peak values for the wave.

Another common method is to use the effective value. This is also known as the Root Mean Squared value.

1

T

2

 

T

0

 

( t) dt

VRMS = --

V

 

For a sinusoidal function we will find that,

VPEAK

VRMS = --------------- = 0.707VPEAK

2

IPEAK

IRMS = ------------- = 0.707IPEAK

2

6.1.2 LR Circuits

• One common combination of components is an inductor and resistor.

page 65

L

(A low pass filter)

 

R

VI

Vo

 

R Vo = VI -------------------

R + jLω

 

 

R

 

 

 

 

 

 

 

 

 

 

(A high pass filter)

 

 

 

 

 

VI

 

 

L

Vo

 

 

 

 

 

 

 

 

 

 

jLω

 

 

 

 

 

 

 

 

 

 

 

V

 

= V

 

 

 

 

 

 

-------------------

 

 

 

 

 

 

o

 

I

R + jLω

 

 

 

 

 

 

 

6.1.3 RC Circuits

• Capacitors are often teamed up with resistors to be used as filters,

page 66

R

 

 

C

 

 

 

(low pass filter)

 

VI

 

 

Vo

1

 

 

 

 

 

 

 

 

 

 

 

 

---------

 

1

 

 

 

 

 

 

Vo =

jω C

=

 

 

 

 

 

 

--------------------1

j-----------------------ω CR + 1

 

 

 

 

 

 

 

R + j---------ω C

 

 

C

VI

R

Vo

(high pass filter)

 

 

 

 

 

 

 

 

 

 

Vo =

R

 

=

jω CR

 

 

 

 

 

R--------------------+ jω

1

j-----------------------ω CR + 1

 

 

 

 

 

 

 

 

 

 

 

C

 

 

6.1.4 LRC Circuits

• These circuits tend to weigh off capacitors and inductors to have a preferred frequency.

page 67

 

R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VI

 

 

 

Vo

 

 

C

 

L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

--------------------------

 

 

 

 

 

 

 

 

 

1

+ jω

 

 

 

 

 

C

 

 

 

j ω L

 

 

 

= V

 

---------

 

 

 

 

V

 

------------------------------------------

 

 

 

 

 

 

 

o

I

 

 

 

 

 

 

 

 

 

 

R + --------------------------

 

1

 

1

 

 

 

 

 

 

 

 

 

+

jω

 

 

 

 

 

 

 

---------

C

 

 

 

 

 

 

jω

L

 

 

 

 

 

 

jω L

 

 

---------------------------------------

jω L

 

 

1 + ( jω C) ( jω L)

 

= V

------------------------------------------------------

 

jω L

 

= ------------------------------------------------

I

 

 

 

jω L + R( 1 – ω 2LC)

 

R +

1---------------------------------------+ ( jω C) ( jω L)

 

6.1.5 LC Circuits

• Inductor capacitor combinations can be useful when attempting to filter certain frequencies,