AM Modulators

Generating standard AM absolutely requires a fundamentally non-linear hardware device. A basic diode and a perfectly tuned LC tank circuit create a highly practical square-law modulator.

Core Concept

The input circuit linearly sums the radio carrier and baseband message signals directly together. This raw summed voltage continuously feeds directly into a standard 1N4148 square-law diode element.

The highly non-linear current curve of the silicon diode mathematically creates all the necessary cross-product terms. A 100 uH inductor and a variable capacitor actively select the desired radio frequencies.

The tuned LC bandpass filter strongly and completely rejects the original baseband and higher-order harmonic signals. This specific diode circuit only works accurately for very small modulation depths.

Key Equations

The fundamental diode current heavily relies on the input voltage terms. The approximate mathematical expansion is i = a*v + b*v^2. The LC tank strictly resonates at f = 1 / (2*pi*sqrt(L*C)).

Given:
Inductor L = 100 uH
Carrier frequency fc = 1 MHz

Why this formula:
The LC tank circuit strictly must resonate exactly at the central carrier frequency.

Formula:
C = 1 / (4 * (pi^2) * (fc^2) * L)

Substitution:
C = 1 / (4 * 9.87 * (10^12) * (100 * 10^-6))

Calculation:
C = 1 / (39.48 * 10^8)
C = 0.000000000253

Final Answer:
Capacitor C = 253 pF

Exam Tip: The standard square-law modulator completely fails at very high modulation index values. Attempting full modulation causes absolutely severe envelope distortion directly due to ignored higher-order non-linearities.

Key Properties

• Non-linear devices like the 1N4148 diode strictly generate the necessary complex frequency cross-products.
• The fundamental square-law circuit inherently produces many unwanted higher-order harmonic distortion terms.
• A tuned LC bandpass filter strictly selects only the desired carrier and the adjacent sideband frequencies.
• The physical inductor and capacitor strictly must resonate precisely at the central carrier frequency.
• This exceptionally simple diode modulator clearly works reliably only for modulation indices strictly below 0.5.

Quick Revision

• A perfectly linear amplifier absolutely cannot ever produce amplitude modulation from simply added signals.
• Baseband and carrier signals clearly sum linearly right before entering the non-linear diode element.
• The LC tank Q-factor strongly determines the strict cutoff of out-of-band high-frequency harmonics.
• High-power AM broadcast stations actively use robust Class C amplifiers instead of simple signal diodes.
• Collector modulation cleanly controls the DC supply voltage to precisely vary the RF output amplitude.
• Exam trap: completely forgetting that the tuned bandpass circuit strictly must be centered perfectly at the carrier frequency, not the low baseband frequency.