The communication by radio, the AM signal is amplified by a power amplifier and fed to the antenna with a characteristic impedance R. The total transmitted power divides itself between the carrier and the upper and lower sidebands. The total transmitted power PT is simply the sum of the carrier power Pc and the power in the two sidebands PUSB (upper sideband) , and PLSB (lower sideband) . This is expressed by this simple equation.

P_{T} = P_{c }+ P_{LSB} + P_{USB}

## Sideband Powers:

The power in the sidebands depends upon the value of the modulation index. The greater the percentage of modulation, the higher the sideband power. Of course, maximum power appeared in the sidebands. When the carrier is 100 percent modulated. The power in each sideband Ps is given by the expression.

Ps = P_{LSB} = P_{USB} = P_{c}(m^{2})/4

Assuming 100 percent modulation where the modulation factor m = 1, the power in each sideband is one-fourth, or 25 percent, of the carrier power. Since there are tow sidebands, their power together represents 50 percent of the carrier power. For example, if the carrier power is 100 watts (W), then at 100 percent modulation, 50 W in each. The total transmitted power then is the sum of the carrier and sideband power or 150 W.

As you can see, the carrier power represents two-third of the total transmitted power assuming 100 percent modulation. With a carrier power of 100 W and a total power of 150 W, the carrier power percentage can be computed.

Carrier Power percentage = 100/150 = 0.667 (or) 66.7%

The percentage of power in the sidebands can be compute in a similar way.

Sideband power percentage = 50/150 = 0.333 (or 33.3%)

The carrier itself conveys no information. The carrier can be transmitted and received, but unless modulation occurs, no information will be transmitted. When modulation occurs, sidebands are produced. It is easy to conclude, therefore, that all the transmitted information is contained within the sidebands. Only one-third of it is literally wasted on the carrier. Obviously, although it is quite effective and still widely used. AM is a very inefficient method of modulation.

At lower percentage of modulation, the power in the sidebands is even less. You can compute the amount of power in a sideband with the previously given expression. Assume a carrier power of 500 W and a modulation of 70 percent. The power in each sideband then is

Ps = P_{c} (m^{2})/4 = 500(0.7)^{2}/4 = 500(0.49)/4 = 61.25 W

At 70 percent modulation, only 61.25 W appears in each sideband for a total sideband power of 122.5 W. The carrier power, of course, remains unchanged at 500 W.

One way to calculate the total Amplitude Modulation power is to use the formula

P_{T} = P_{c}(1 + m^{2}/2)

Where Pc = unmodulated carrier power

m = modulation index

For example, if the carrier power is 1200 W and the percentage of modulation is 90 percent, the total power is

P_{T} = 1200( 1 + 0.9^{2 }/2) = 1200(1.405)= 1686 W

If you subtract the carrier power, this will leave the power in both sidebands.

P_{T} = P_{c} + P_{LSB} + P_{USB}

P_{LSB} + P_{USB} = P_{T} – P_{c}

= 1686 – 1200 = 486 W

Since the sideband powers are equal, the power I each sideband is 486/2 = 243 W. In practice, 100 percent modulations is difficult to maintain. The reason for this is that typical information signals, such as voice and video, do not have constant amplitudes. The complex voice and video signals vary so 100 percent modulation only occurs on the peaks of the modulating signal. For this reason, the average sideband power is considerably less than the ideal 50 percent produced by full 100 percent modulation. With less sideband power transmitted, the received signal is weaker and communication is less reliable.

Despite its inefficiency, Amplitude Modulation (AM ) is still widely used because it is simple and effective. It is used in AM radio broadcasting, CB radio, TV broadcasting, aircraft communication, and computer modems.

There are three ways to calculate the power dissipated in a load. These are

P = V(I)

P = V^{2}/R

P = I^{2}R

Simply select the formula for which you have the values of current, voltage, or resistance. In an AM radio transmitting station. R is the load resistance, which is an antenna. To a transmitter, the antenna looks like a resistance. Although an antenna is not actually a physical resistor, it does appear to be one. This resistance is referred to as the *characteristic resistance of antenna*.

### Power Calculations:

A common way to determine modulated power is to measure antenna current. Current in an antenna can be measure because accurate radio-frequency current meters are available. For example, if you know that the un-modulated carrier produces a current of 2.5 A in an antenna with a characteristic resistance of 23 Ohm, the power is:

P = I^{2}R = (2.5)2(73) = 6.25(73) = 456.25 W

If the carrier is modulated, the antenna current will be higher because os the additional power in the sidebands. The total antenna current I_{T} is

I_{T = } I_{c} √ (1 + m^{2}/2)

Where Ic = un-modulated carrier current

m = modulation index

If the un-modulated carrier current is 4 and the percentage modulation is 70 percent, the total output is

I_{T} = 4 √(1 + 0.7^{2}/2)

= 4 √1.245

= 4(1.116) = 4.46 A

The total AM power then is

P_{T} = (I_{T})^{2}R

To determine the total power, monitor the total modulated antenna current and make the calculation above, given the antenna resistance.

If you measure both the modulated and the unmodulated carrier antenna current, you can compute the percentage of modulation by using this formula

m = √2|(I_{T}/I_{c})^{2} – 1 |

Assume that you measured the unmodulated carrier current and found it to be 1.8 A. With modulation, the total current was 2 A. The percentage of modulation is:

68.4 %