Amplitude modulation (AM) is an electronic communication method where a carrier wave's strength (amplitude) alters in proportion to the data signal, like audio or voice wave. While the carrier's frequency stays the same, its height grows and shrinks to carry the message.
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The AM envelope refers to the outputted modulation signal's border lines.
An AM wave has 3 components: The fundamental frequency (or just "fundamental"), unmodulated carrier (fC), or the carrier frequency (fC), the upper sideband (USB) and the lower sideband (LSB).
The message/modulation/modulating/data/baseband signal or frequency is the original info signal (often low frequency), being fed to the mixer. It can be speech or music.
The carrier signal is a high-frequency sine wave used to carry the info over a distance.
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An AM modulated signal's maximum amplitude can be defined mathematically as the sum of the carrier and message signal's amplitude: Amax = AC+Am.
An AM modulated signal's minimum amplitude can be defined mathematically as the difference of the carrier and message signal's amplitude: Amin = AC-Am.
The AM bandwidth (BW) is the length from the USB the LSB, with the carrier at the center of the BW, mathematically defined as BW = 2*fm = [4] (fC-fm) - (fC+fm) = fUSB - fC
fc = carrier frequency
fm = message/modulation frequency
The USB is the upper sideband (on the right) of the fundamental, mathematically defined as: USB = fC-fm
The LSB is the lower sideband (on the left ) of the fundamental, mathematically defined as: LSB = fC+fm
Each sideband's bandwidth is calculated as VC/2.
The modulation frequency, here, is the difference of either sideband frequency to the carrier frequency.
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[Q1] Fig. 1
fm = fUSB - fC = 10.5kHz - 10kHz = 500 Hz
This signal's bandwidth is: BW = 2*500Hz = 1 kHz.
Peak power frequency values The peak of the sidebands and the carrier frequency can are often measured in dBm in the spectrum analyzer. We must often convert these values in milliwatt units, via the formula PmW = 10P/10
In Fig. 1, the sideband powers is -11.14 dBm, which is 10-11.14/10 = 0.077 mW. So the total sidebands of the signals are 13mW*2 + 10-2.035/10 = 0.154 + 0.63 = 0.784 mW or 10*log(0.784) = -1.06 dBm.
Peak power frequency values with resistance loads When calculating voltage, power, and frequency parameters in RF and communications systems with resistive loads, the relationships depend on whether we're working in the time domain (oscilloscopes) or frequency domain (spectrum analyzers).
The VRMS value across a resistance load is defined as: VRMS = √(PW x R), since Power across a purely resistive load relates to VRMS voltage P = VRMS2/R, where recall that VRMS is just the regular (average) voltage for an AC wave (like DC voltages), thus using the regular DC power formula: P = V2/R.
The modulation index (m) indicates by how much (in percentage) modulation the modulation wave changes over the carrier signal, mathematically defined as:
m = Am/AC
Am = message signal
AC = carrier signal
The modulation depth is the modulation index expressed in percentage, instead of a ratio, mathematically defined as: Am/AC x 100% = m x 100%.
E.g., if a message signal of 2.3 V amplitude is mixed to a carrier signal of 3.59 V amplitude, then the index is: m = 2.3V/3.59V = .5571;
And the modulation depth is 55.71%
Modulation index/depth via envelope We can alternatively calculate the modulation depth/index via the resulting modulation signal's min and max amplitudes.
The formula for this is: m = (Amin-Amax)/(Amin+Amax)
E.g., in this case the max is 432 mV and the min is 63 mV. The index is: (432mV-63mV)/(432mV+63mV) = .75;
And the depth is 75%.
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[3] E.g., in this case the max is 2 V and the min is ~0.01, The index is: (2-.01)/(2+.01) = 0.99;
And the depth is 99%, almost 100% modulation.
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Modulation index/depth via sidebands powers We can also calculate the modulation index/depth via sidebands.
The formula for this is: m = 2 x 10(PSB - PC)/20 x 100%, where
PSB = sideband power (in dB)
PC = carrier power (in dB)
Breaking the formula down: Knowing the sideband formula is: PSB = PC + 20 log10(m/2), rearranged into (PSB - PC)/20 = log10(m/2) → 2 x 10(PSB - PC)/20 = 2 x 10ΔP/20.
ΔP = power difference between sideband and carrier power - always ensure that the reference value (the carrier) is subtracted from the measured value (the sideband):
PSB -PC
E.g., in this spectrum analyzer screen measurement, the carrier signal power is -2.035 dBm and the sideband power is -11.14 dBm.
Calculating the power difference: ΔP = -11.14-(-2.035) = -9.105 dB
Then modulation index is: 2 x 10-9.105/20 = 0.7;
And the depth is 70%.
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Overmodulation and undermodulation The carrier can be seen as a wave whose amplitude is controlled by the message.
When the index or depth is over the value of 1 or 100% respectively, it's either of these 3 conditions:
m < 1 → undermodulation
m = 1 → 100% modulation depth, ideal max for ordinary AM
m > 1 → overmodulation, causing distortion
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Through AM, the AM modulator or mixer combines ("multiplies") the message and carrier signal. The amplitude of the carrier changes according to the message signal's instantaneous amplitude, while the carrier's frequency stays essentially constant.
The modulator outputs the modulated AM signal, a high-frequency carrier whose envelope follows the shape of the message signal. This signal can then be transmitted through an antenna.
The process of the mixer multiplying the message/modulating and carrier signals is defined mathematically as: cos(2πfCt)×cos(2πfmt).
What process does diagram depicts? - amplitude modulation (AM)
What does ‘X’ represents here? - frequency mixer
Which one is LF signal in diagram? - top left signal, the modulating/information/message signal
Which one is RF signal in diagram? - bottom left, carrier wave
Which left signal is modulated? - carrier
Which left signal is unmodulated? - message signal (top left)
How does the mixer merge carrier wave to signal? - by mathematically multiplying the wave to signal
What’s an envelope in a signal? - curve outlining/borders in oscillating carrier waves
What does the space inside the envelope of an AM modulated carrier signal represent? - it’s pure carrier energy – IO of info, it provides raw power for music/audio and steady baseline to read sound accurately
Whose ampltitude does the sum of modulated carrier wave’s Vmax and Vmin represents? - unmodulated carrier’s amplitude
Whose ampltitude does the difference of modulated carrier wave’s Vmax and Vmin represents? - modulating/message signal’s amplitude
Modulation index formula in AM via carrier and message signal’s amplitude? - Vm/VC, which equals (Vmax - Vmin)/(Vmax + Vmin)
What happens when you view the sine waves in time domain from the side (left and right)? - the waves are seen
Note: Althought a mixer "multiplies" the carrier and the modulating signal, unlike what the AM index formula m = Am/AC suggests, note that the mixer actually multiplies the 2 signals as waveforms:
A carrier amplitude's instantaneous value changes according to the modulating signal's amplitude, as expressed by the AM modulating index formula m = Am/AC.
This can be proven by calculating modulated signal's max and min amplitudes via its modulating and carrier signal's own amplitudes: Amax = AC+Am and Amin = AC-Am.
E.g., if AC = 10 V and Am = 2 V, where the index is m = 2V / 10V = 20%, and:
Amax=2V + 10V = 12 V and Amax=10V - 2V = 8 V.
But decreasing AC to 6 V, while Am stays at 2 V, increases the max modulated amplitude Amax = 6V + 10V = 16 V, but decreases the min amplitude Amin = 16V - 2V = 14 V, and now with the index at 2V/6V = 33%, meaning the modulating signal is now 40% of the carrier.
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