Envelope Detector RC Constant
Size the diode-detector RC so an AM envelope tracks cleanly — big enough to smooth carrier ripple, small enough to dodge diagonal clipping.
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The engineering
A diode envelope detector charges C on carrier peaks and lets R bleed it down between them. The RC product has to thread a window: too small and the output rides carrier ripple; too large and the capacitor can't discharge fast enough to follow the falling side of the envelope — the diode cuts off and the output slides down a straight RC decay instead of the audio. That failure is diagonal clipping, and it gets worse at high modulation index and high modulation frequency, which is exactly what the √(1−m²)/(2πf_m·m) limit captures.
This card takes 10 carrier periods as the ripple floor and splits the window at the geometric mean, then converts to a capacitor for your load resistor. Sanity check: at a 455 kHz IF with 5 kHz audio and m = 0.8 the window is only ~22–24 µs wide — deep modulation at a low IF leaves almost no margin. If the window closes entirely, move to a higher IF or accept a lower usable modulation depth.
Remember R here is the total DC load the diode sees, including the volume-pot and AGC network in parallel. A mismatch between the detector's DC and AC load causes negative-peak clipping — a separate failure this card doesn't model, but one to check right after the RC math works out.
Where this math comes from
The envelope detector is as old as broadcast radio itself. Greenleaf Whittier Pickard's 1906 silicon cat's-whisker crystal was the first mass-market rectifying detector, and every crystal set that followed was an envelope detector with an RC picked by ear. When Edwin Armstrong's 1918 superheterodyne fixed the detection frequency at a known IF, the RC choice stopped being a shrug and became a design calculation.
The diagonal-clipping criterion — that RC must stay under √(1−m²)/(ω_m·m) or the capacitor's discharge line falls behind the envelope — worked its way through the receiver-design literature of the 1930s and 40s, with Frederick Terman's Radio Engineering giving it wide circulation. Krauss, Bostian, and Raab's Solid State Radio Engineering (1980) stated it in the compact form this card evaluates, and it remains the standard homework check for anyone hanging a diode off an IF strip.
- 1904John Ambrose FlemingPatents the thermionic diode valve — the first reliable AM rectifier.
- 1906Greenleaf Whittier PickardSilicon cat's-whisker crystal detector puts envelope detection in every crystal set.
- 1918Edwin ArmstrongSuperheterodyne fixes detection at a known IF, making the RC a real design number.
- 1932Frederick TermanRadio Engineering spreads the quantitative treatment of detector distortion.
- 1980Krauss, Bostian & RaabSolid State Radio Engineering codifies the √(1−m²)/(ω_m·m) diagonal-clipping limit.
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