AM DSB-FC

Double sideband full carrier AM, commonly written as DSB-FC or simply standard AM, is the conventional form of amplitude modulation in which the carrier and both sidebands are transmitted together. It is the form of AM used in commercial medium-wave broadcasting and is the baseline against which all other AM variants such as DSB-SC, SSB, and VSB are compared.

Core Concept Explanation

In DSB-FC, the full (unattenuated) carrier is always present in the transmitted signal regardless of whether a message is being sent. This differentiates it from DSB-SC (suppressed carrier), where the carrier is deliberately removed. The prefix double sideband refers to the fact that both the upper sideband (USB) and lower sideband (LSB) are transmitted. Both sidebands are present and carry identical copies of the message information.

The mathematical form of DSB-FC is: s(t) = Ac [1 + mu*m(t)] cos(2*pi*fc*t), where m(t) is the normalized message signal with peak value 1. The term [1 + mu*m(t)] represents the time-varying envelope. For the envelope to remain positive at all times (a requirement for distortion-free envelope detection), the condition 1 + mu*m(t) greater than 0 must hold for all t. Since the minimum of m(t) is -1 for a normalized signal, this requires mu less than or equal to 1.

The key advantage of the full carrier is that it enables the use of a simple envelope detector at the receiver, which extracts the message by following the amplitude envelope of the received signal. The envelope detector consists of a half-wave rectifier (diode) followed by a low-pass RC filter. This circuit is inexpensive to manufacture, which is why DSB-FC remains the standard for mass-market AM broadcasting.

Mathematical Expression

Expanding the DSB-FC signal: s(t) = Ac*cos(2*pi*fc*t) + (mu*Ac/2)*cos(2*pi*(fc+fm)*t) + (mu*Ac/2)*cos(2*pi*(fc-fm)*t). The three components and their powers are: Pc = Ac^2/2 (carrier), PUSB = PLSB = mu^2*Ac^2/8 (each sideband). Total power Pt = Pc*(1 + mu^2/2). The spectral efficiency of DSB-FC is low because the bandwidth occupied is 2*fm while useful information bandwidth is only fm (since both sidebands carry the same information, one sideband is redundant).

For coherent detection of DSB-FC, the receiver multiplies the received signal by a locally generated carrier of the same frequency and phase, then applies a low-pass filter. The coherent detector works for all values of mu including mu greater than 1, making it immune to overmodulation distortion. However, coherent detection requires carrier synchronization at the receiver, which is more complex and expensive than the envelope detector.

Practical Understanding

Classic AM broadcasting on medium wave (530-1600 kHz) and shortwave bands uses DSB-FC. The standard channel bandwidth is 9 kHz in regions following ITU Region 1 (Europe, Africa, Asia) and 10 kHz in the Americas. Each station's sidebands must fit within this allocation. The full carrier also serves as a pilot signal that the receiver uses to automatically set gain (via automatic gain control, AGC) and fine-tune to the station.

Compared to DSB-SC, the DSB-FC signal requires approximately 50% more transmitter power at mu = 1 to achieve the same SNR in the sidebands at the receiver. This is acceptable for the broadcast scenario but unacceptable for point-to-point links where transmitter power and bandwidth are limited. This motivated the development of SSB and DSB-SC for telephony applications and satellite links.

Given:
Carrier frequency fc = 1 MHz, message frequency fm = 5 kHz, modulation index mu = 0.7
Carrier power Pc = 1000 W (into 50 ohm load)

Why this formula applies:
DSB-FC power formula Pt = Pc*(1 + mu^2/2). Antenna current ratio for transmitter power check.

Formula:
Pt = Pc * (1 + mu^2/2)
It/Ic = sqrt(Pt/Pc) = sqrt(1 + mu^2/2)

Substitution:
mu^2 = 0.49, mu^2/2 = 0.245
Pt = 1000 * (1 + 0.245) = 1000 * 1.245

Calculation:
Pt = 1245 W
Total sideband power = 1245 - 1000 = 245 W
Each sideband = 122.5 W
Bandwidth = 2 * 5 kHz = 10 kHz (996 kHz to 1006 kHz occupied)
It/Ic = sqrt(1.245) = 1.115

Final Answer:
Total transmitted power = 1245 W, with 1000 W in carrier and 245 W in both sidebands. Bandwidth = 10 kHz. Antenna current increases by factor 1.115 when modulated.

Exam Tip: GATE distinguishes DSB-FC from DSB-SC by the presence of the carrier term in the spectrum. DSB-FC demodulation using an envelope detector requires mu less than or equal to 1. DSB-SC demodulation requires coherent detection because there is no carrier to guide an envelope detector. Remember DSB-SC has zero power at carrier frequency fc in its spectrum.

Quick Revision

• DSB-FC signal: s(t) = Ac[1 + mu*m(t)]*cos(2*pi*fc*t). Both sidebands and full carrier are present.
• Spectrum: carrier impulse at fc (amplitude Ac), sideband impulses at fc+/-fm (amplitude mu*Ac/2).
• Total power: Pt = Pc*(1 + mu^2/2). Carrier power Pc = Ac^2/2R.
• Bandwidth: BW = 2*fm (single tone), 2*W (general). Both sidebands carry identical information.
• Envelope detection requires mu less than or equal to 1. No carrier synchronization needed at receiver.
• Antenna current at modulation: It = Ic*sqrt(1 + mu^2/2).
• Trap: DSB-FC vs DSB-SC: full carrier present in DSB-FC, carrier absent in DSB-SC. Envelope detector works only for DSB-FC.