AM, DSB-SC, SSB-SC, SSB-LC & VSB Power Calculator | Modulation Power Simulator

 

1. Start with normal AM

For AM:

$$P_T=P_C\left(1+\frac{\mu^2}{2}\right)$$

The two sidebands together have power:

$$P_{SB}=\frac{\mu^2}{2}P_C$$

And because the two sidebands are equal:

$$P_{USB}=P_{LSB}=\frac{\mu^2}{4}P_C$$

So for $\mu=1$:

$$P_{USB}=P_{LSB}=\frac14P_C$$

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2. What does VSB do?

VSB = Vestigial Sideband.

It keeps:

• one complete sideband

• a small portion of the other sideband

For example, suppose we transmit:

• complete USB → $1/4P_C$

• 50% of LSB → $1/8P_C$

Then total sideband power is:

$$P_{SB,VSB}=\frac14P_C+\frac18P_C$$ $$=\frac38P_C$$

Therefore total VSB power is:

$$P_T=P_C+\frac38P_C$$ $$\boxed{P_T=\frac{11}{8}P_C}$$

for $\mu=1$ and a 50% vestige.

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3. General idea

If the vestigial sideband contains a fraction $k$ of one sideband, then:

$$P_{SB,VSB} = \frac{\mu^2}{4}P_C + k\frac{\mu^2}{4}P_C$$

Therefore:

$$\boxed{ P_{T,VSB} = P_C\left[1+\frac{\mu^2}{4}(1+k)\right] }$$

where $0\leq k\leq1$.

For example:

VSB	$k$	Total power
One complete sideband only (SSB)	0	$P_C(1+\mu^2/4)$
50% vestige	0.5	$P_C(1+3\mu^2/8)$
Both complete sidebands (AM)	1	$P_C(1+\mu^2/2)$

So the important thing is:

$$\boxed{\text{AM: }1+\frac{\mu^2}{2}}$$

but for VSB, you need to know how much of the vestigial sideband is transmitted.

4. DSB-SC

DSB-SC = Double Sideband Suppressed Carrier

It transmits:

• USB ✅

• LSB ✅

• Carrier ❌

For a sinusoidal message with modulation index $\mu$, each sideband has power

$$P_{USB}=P_{LSB}=\frac{\mu^2}{4}P_C$$

Therefore total power is

$$P_T=\frac{\mu^2}{4}P_C+\frac{\mu^2}{4}P_C$$ $$\boxed{P_T=\frac{\mu^2}{2}P_C}$$

For $\mu=1$:

$$\boxed{P_T=\frac12P_C}$$

Notice: there is no carrier power because the carrier is suppressed.

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5. SSB-SC

SSB-SC = Single Sideband Suppressed Carrier

It transmits:

• USB or LSB ✅

• Other sideband ❌

• Carrier ❌

So only one sideband remains.

Therefore:

$$\boxed{P_T=\frac{\mu^2}{4}P_C}$$

For $\mu=1$:

$$\boxed{P_T=\frac14P_C}$$

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3. Compare all three

Modulation	Carrier	USB	LSB	Total power
AM	✅	✅	✅	$\displaystyle P_C(1+\frac{\mu^2}{2})$
DSB-SC	❌	✅	✅	$\displaystyle \frac{\mu^2}{2}P_C$
SSB-SC	❌	✅	❌	$\displaystyle \frac{\mu^2}{4}P_C$

$$\boxed{\text{Carrier}+\text{USB}+\text{LSB}}$$

For $\mu=1$:

• Carrier = $P_C$

• USB = $P_C/4$

• LSB = $P_C/4$

So:

AM:

$$P_C+\frac{P_C}{4}+\frac{P_C}{4} =\boxed{\frac32P_C}$$

DSB-SC:

$$\frac{P_C}{4}+\frac{P_C}{4} =\boxed{\frac12P_C}$$

SSB-SC:

$$\frac{P_C}{4} =\boxed{\frac14P_C}$$

So if you remember each sideband = $\mu^2P_C/4$, you can derive almost everything instead of memorizing separate formulas.