update

README.md

@@ -1,14 +1,14 @@
 # ambium
 
-Analog white-noise generator. Single **+12 V** supply, breadboard-friendly.
-Broadband hiss to a **4 Ω speaker** via a TIP120 driver.
+Analog brown-noise generator. Single **+12 V** supply, breadboard-friendly.
+Deep filtered rumble to a **4 Ω speaker** via a TIP120 driver.
 
 Reference designators and model numbers are consistent across every diagram, the
 BOM, and the connection list — the connection list is the authoritative netlist.
 
 ## Parts
 
-- **U1** = LM358 (dual op-amp, DIP-8). U1B = amp. U1A unused (inputs tied to VREF).
+- **U1** = LM358 (dual op-amp, DIP-8). U1B = amp + brown shaping. U1A unused (parked).
 - **Q1** = 2N3904 (NPN). Avalanche noise source.
 - **Q3** = TIP120 (NPN Darlington, TO-220). Class-A speaker driver.
 
@@ -19,9 +19,9 @@ BOM, and the connection list — the connection list is the authoritative netlis
 ## Signal chain
 
 ```
- [noise]        [amplify]        [driver]
-Q1 2N3904  →  U1B LM358 ×1000 →  Q3 TIP120  →  4Ω speaker
- NOISE          AMP               (class A)
+ [noise]      [amp + brown]      [driver]
+Q1 2N3904  →  U1B LM358 −6dB/oct →  Q3 TIP120  →  4Ω speaker
+ NOISE         AMP                   (class A)
 ```
 
 Legend:
@@ -88,26 +88,40 @@ internal, don't label it.
 
 ---
 
-## Stage 2 — Amplifier ×1000 (U1B, Rin1, Rf1)
+## Stage 2 — Amplifier + brown shaping (U1B, Rin1, Rf1, Cf1)
 
-Inverting amp, gain ≈ −Rf1/Rin1 = ×1000, centred on VREF. Clips into the rails at
-this gain — that's the loud hiss fed to the driver. Too harsh? Drop Rf1 (e.g. 470k).
+Single inverting amp, low-frequency gain −Rf1/Rin1 = ×1000, centred on VREF. A feedback
+cap Cf1 across Rf1 makes it a leaky integrator: flat gain below the corner, then −6 dB/oct
+above it. That −6 dB/oct slope turns white noise into **brown**. One stage does gain and
+browning together — no separate integrator needed.
+
+- corner fc = 1/(2π·Rf1·Cf1) ≈ **19 Hz** with Rf1 1M, Cf1 8.2nF.
+- below fc: flat ×1000. above fc: −6 dB/oct, reaching unity (×1) at ~20 kHz.
+- so the whole audible band (20 Hz–20 kHz) rides the brown slope; peak gain ×1000 at the
+  bottom, rolling off inaudible ultrasonics at the top for free.
+
+**Why not a flat ×1000 stage?** LM358 GBW = 1 MHz → a flat ×1000 stage has only 1 MHz/1000
+≈ **1 kHz** bandwidth, collapsing the band (measured ~27 mV pp at AMP). Here Cf1 makes the
+demanded gain *fall* with frequency, so the op-amp GBW is never the limit — the RC feedback
+does the shaping, not the op-amp rolloff.
 
 LM358 DIP-8, notch at top, pin 1 top-left. Amp = **unit B** (pins 5/6/7).
 
 ```
-                          ┌────∪────┐
-           ┌───── OUT A  1┤●        ├8  V+   ──── +12V
-           └───── IN− A  2┤         ├7  OUT B ──●──────────────►  AMP
-        VREF ──── IN+ A  3┤  LM358  ├6  IN− B ──●
-         GND ──── V−     4┤         ├5  IN+ B ──── VREF
-                          └─────────┘
+                    ┌─────∪────┐
+         OUT A   1 ─┤●         ├ 8  V+     ──── +12V
+         IN− A   2 ─┤          ├ 7  OUT B  ──●──────────────►  AMP
+  VREF ─ IN+ A   3 ─┤  LM358   ├ 6  IN− B  ──●
+   GND ─ V−      4 ─┤          ├ 5  IN+ B  ──── VREF
+                    └──────────┘
 
-  feedback (pin 7 ↔ pin 6):   pin 7 ●──[Rf1 1M]──● pin 6      Rf1 ∥ Cf1
-                              pin 7 ●──[Cf1 22pF]─● pin 6      anti-osc, limits BW
-
-  input:                      NOISE ─[Rin1 1k]──● pin 6
+  feedback (pin 7 ↔ pin 6):  pin 7 ●──[Rf1 1M]────● pin 6     Rf1 ∥ Cf1
+                             pin 7 ●──[Cf1 8.2nF]──● pin 6     brown slope, corner ~19 Hz
+  input:                     NOISE ─[Rin1 1k]──● pin 6
 ```
+DC handling: C1 blocks DC into Rin1, so the op-amp's own offset sees unity gain — output
+sits at VREF (6 V), no railing.
+
 Unit A unused → park as a follower so it can't oscillate: pin 3 → VREF, pin 2 → pin 1.
 Power/decoupling (whole chip, once): pin 8 → +12V, pin 4 → GND. 47µF bulk + 0.1µF at
 pin 8.
@@ -158,12 +172,12 @@ TIP120 pinout (TO-220, face up, pins down): **1 Base · 2 Collector · 3 Emitter
 | R1 | 100k | resistor | avalanche current limit |
 | R2, R3 | 10k | resistor | VREF divider |
 | Rin1 | 1k | resistor | amp input |
-| Rf1 | 1M | resistor | amp feedback (×1000) |
+| Rf1 | 1M | resistor | amp feedback (low-freq gain ×1000) |
 | Rb1, Rb2 | 10k | resistor | Q3 base bias (~6 V) |
 | Re | 22Ω 3W | resistor | Q3 idle-current set |
 | C1 | 10µF | electrolytic | noise coupling |
 | Cref | 10µF | electrolytic | VREF bypass |
-| Cf1 | 22–100pF | ceramic | amp feedback / anti-oscillation |
+| Cf1 | 8.2nF | film / ceramic | feedback / brown shaping (−6dB/oct, corner ~19 Hz) |
 | Cc | 10µF | electrolytic | AMP → base coupling |
 | Cout2 | 470µF ≥16V | electrolytic | speaker coupling (big, for lows) |
 | — | 0.1µF | ceramic | LM358 decoupling |
@@ -182,7 +196,7 @@ VREF   : R2.2, R3.1, Cref.+, U1B.IN+(5), U1A.IN+(3)
          U1A.OUT(1) = U1A.IN−(2)                  (spare amp parked as follower)
 (src)  : R1.2, Q1.emitter, C1.+                 (internal raw-noise node)
 NOISE  : C1.−, Rin1.1                            (after C1)
-AMP    : U1B.OUT(7), Rf1, Cc.1                   (Rin1.2, Rf1, U1B.IN−(6) = summing)
+AMP    : U1B.OUT(7), Rf1, Cf1, Cc.1              (Rin1.2, Rf1, Cf1, U1B.IN−(6) = summing)
 base   : Cc.2, Rb1.2, Rb2.1, Q3.base             (~6 V bias)
 SPKR   : Q3.emitter, Re.1, Cout2.+ ;  Cout2.− → speaker → GND
 Q1     : collector = no-connect
@@ -194,14 +208,15 @@ Q1     : collector = no-connect
 
 1. **VREF** — confirm ~6.0 V.
 2. **Noise (R1, Q1)** — scope Q1 node → hiss (~mV). None? swap 2N3904 or raise supply to 12–15 V.
-3. **Amp (U1B)** — scope AMP → loud hiss (~volts).
+3. **Amp (U1B)** — scope AMP → deep rumble (~volts), darker than the raw Q1 hiss (that's the brown slope).
 4. **Driver (Q3)** — feed AMP through Cc. Speaker hisses. Q3 warm, not hot; too hot → raise Re.
 
 ## Tuning
 
 | Want | Change |
 |------|--------|
-| Louder | ↑ Rf1 (watch clipping) |
-| Less harsh | ↓ Rf1 |
+| Louder | ↑ Rf1 (raises low-freq gain; watch clipping) |
+| Darker / deeper | ↑ Cf1 (lowers corner, more brown) |
+| Brighter (toward white) | ↓ Cf1 (raises corner) |
 | Cooler driver | ↑ Re |
 | More headroom | ↓ Re (hotter — bigger heatsink) |