AC Voltage Equation (AVE)

In AC voltage or AC waves we usually hear terms like the following:

  • Frequency units ... Hz = CPS (cycles per second)
  • RMS (root means square) or what we often see on multitester measurements, for example a sinusoidal wave
  • Instantaneous
  • Average.


Equations On Sinouside Waves

Information:

  • V = Voltage, V = I * R
  • ? = Omega, 2?f = 2?/F
  • I = Current, I = V/R

Getting to Know In-Phase Signals


In-Phase Signal

Problems example

A wave has a voltage equation (v) 5 sin 2000 t, determine!

Modulation

It is the process of superimposing a low frequency signal (information signal) on a high frequency signal / radio frequency (RF) which causes the amplitude / frequency of the RF to change.

High Frequency (HF) = Radio Frequency (RF)

Both frequencies are the same, namely the carrier frequency.

Low Frequency (LF) = Audio Frequency (AF)

Both frequencies are the same, namely the frequency carried.

Types of Modulation

  • Amplitude Modulation (AM)
  • Angle Modulation is divided into 2, namely: Frequency Modulation (FM) and Phase Modulation.

Amplitude Modulation (AM)

It is a superimposition of an AF signal on an RF signal which causes the amplitude of the RF signal (carrier) to change according to changes in the modulation signal.

Example:

m can also be found using the formula:

m = Vm / Vc

Information:

  • Vm = Modulation voltage (Af), with units "rms"
  • Vc = Carrier voltage, with units "rms"

AF Wave Formula

Vm = Vm sin ?mt

RF Wave Formula

Vc = Vc sin ?ct

So,

VAM = Vc = Vc sin ?ct + (m*Vc)/2 * cos (?c-?m)*t - (m*Vc)/2 cos (?c+?m)*t

Exercises

An audio sine wave has the equation Vm = 2 sin 4000t, if the amplitude wave is superimposed on the RF wave and causes the RF wave to change (AM).

Determine:

  • The instantaneous voltage equation of the AM wave that occurs
  • Modulation index
  • Modulation wave frequency
  • Carrier wave frequency.

Solution:

Equation 1

VAM = Vc = Vc sin ?ct + (m*Vc)/2 * cos (?c-?m)*t - (m*Vc)/2 cos (?c+?m)*t
VAM = 6 sin 4000t + (m*6)/2 cos (4000-1000)*t - (m*6)/2 cos (4000+1000)*t
VAM = 6 sin 4000t + 3m cos 3000t - 3m cos 5000t

m = Vm/Vc = 2/6 = 1/3, maka;

Equation 2

VAM = 6 sin 4000t + 3m cos 3000t - 3m cos 5000t
VAM = 6 sin 4000t + 3*1/3 cos 3000t - 3*1/3 cos 5000t
VAM = 6 sin 4000t + cos 3000t - cos 5000t

Vm = 2 sin 1000t
Vm = Vm sin ?mt
?m = 1000

2?fm = 1000
fm = 1000/2?f = 0.159 * 1000 = 159

? = kecepatan sudut atau "Angle Velority", dengan satuan (rad/s).
1pm = putaran / min
1pm = 2? rad / 60s
1pm = ? / 30 * rad/s
?c = 2?fc = Fc

Power On AM Waves

Pt = pc (1 + m2/2)
Pt = pc + m2/2 * pc
Pt = Daya Carrier + Daya Side Band

Information:

  • pc = power on carrier
  • m = modulation index
  • 0

Question 2

An AM transmitter has a power output of 100 watts, transmitted with m = 0.6. Calculate the power transmitted through the transmitting antenna.

It is known:

PC = 100 watts
m = 0.6

Asked:

Pt = ?

Solution:

Pt = Pc + mxm/2 x PC
   = 100 + 0.6 x 0.6 /2 x 100
   = 100 + 0.36/2 x 100
   = 118 watts

Note! - the power on the AM wave is determined by the modulation index value (m), the greater the value of m, the greater the value of Pt, and vice versa.

The power transmitted by the AM transmitter is 236 KW, if the unmodulated power is 200kw. Determine the depth of modulation!

It is known: 

Pt = 236 kw
pc = 200kw

Asked, m = ?

Solution:

Pt = pc (1 + m2/2)
236 = 200 (1 + m2/2)

m2= (236/200-1) 2
m2= (1.18 - 1 ) 2
m2= 0.36
m2= 0.6

Current in AM Waves

From the formula:

Question 3

The antenna of an AM transmitter current = 8A, if only the carrier is transmitted, the current becomes 8.93. If the carrier is modulated simultaneously, determine the modulation percentage!

Answer:


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