================================================================================ SCHEMATIC: HEADPHONE MATCHING TRANSFORMER TM-CR-001 Rev A Impedance matching: 1000:8 Ω (crystal radio detector to low-Z headphones) AM broadcast audio; passive; no battery ================================================================================ OVERVIEW -------- Crystal radio detector circuits develop audio signal across a high-impedance load (detector Z ≈ 10 kΩ – 2 MΩ depending on design). Modern headphones are 8–32 Ω. Without a matching transformer, the impedance mismatch causes 90–99% of available audio power to be lost. IMPEDANCE MATCHING REQUIREMENT: Detector (source) impedance: Z_s ≈ 10 kΩ – 200 kΩ (typical crystal radio) Headphone (load) impedance: Z_L = 8 Ω (common low-Z headphone) Required transformer turns ratio: N = √(Z_s / Z_L) For Z_s = 1000 Ω, Z_L = 8 Ω: N = √(1000/8) = √125 = 11.18:1 For Z_s = 2000 Ω, Z_L = 8 Ω: N = √(2000/8) = √250 = 15.81:1 For Z_s = 5000 Ω, Z_L = 8 Ω: N = √(5000/8) = √625 = 25.00:1 For Z_s = 10000 Ω, Z_L = 8 Ω: N = √(10000/8) = √1250 = 35.36:1 For Z_s = 20000 Ω, Z_L = 8 Ω: N = √(20000/8) = √2500 = 50.00:1 For Z_s = 32 Ω, Z_L = 8 Ω: N = √(32/8) = √4 = 2:1 (high-Z magnetic earphone to 8Ω; rarely needed) RULE: Use N = 50:1 for crystal radio with 8 Ω phones (safe conservative match). This assumes Z_detector ≈ 20 kΩ (typical loaded detector output). EARPHONE TYPES AND MATCHING: Type Impedance Transformer needed? Notes ---- --------- ------------------ ----- Crystal earphone 50 kΩ–2 MΩ NO Plug in directly Piezoelectric disk 100 kΩ NO Very sensitive High-Z magnetic 2000–4000 Ω NO (or 2:1 max) Old radio headphones Low-Z magnetic 200–600 Ω 5:1 to 8:1 TV/communication type Modern headphones 8–32 Ω 35:1 to 50:1 Most common today Speaker (6") 8 Ω 50:1 Requires strong station DO NOT connect 8 Ω headphones directly to crystal radio detector. The 8 Ω load will completely kill tank circuit Q and selectivity. ================================================================================ TRANSFORMER DESIGN — TOROIDAL CORE ================================================================================ CORE SELECTION: Audio transformer frequency range: 300 Hz – 6000 Hz (adequate for AM voice) For hi-fi: 100 Hz – 10 kHz (use larger core or better material) Core requirements: High permeability (µ_i > 1000) for low-frequency audio Low core loss at audio frequencies NOT ferrite designed for RF (too lossy at audio; those are MHz types) Recommended cores: Manufacturer Part# Material µ_i OD×ID×H (mm) Notes ----------- ----- -------- --- ----------- ----- Fair-Rite 5977002701 Mix 77 2000 13.8×7.3×6.4 Best choice Amidon T-94A-77 Mix 77 2000 24×14×10 Larger; easier Mouser/Kemet T35-77 Mix 77 2000 9×5×3.5 Small; tricky Salvage audio output laminated 500+ varies Old radios/TVs transformer silicon steel any toroid > 10mm Fair-Rite Mix 77 binocular core BN-73-302: Material: Mix 73 (µ_i = 2500), for audio/LF; 0 – 1 MHz OD = 13 mm; also good for this transformer. AVOID: Mix 43, Mix 31 (RF ferrite; lossy at audio). Mix 61 (antenna rod material; very lossy at audio). TURNS RATIO N = 50:1 (Z_s = 20 kΩ → Z_L = 8 Ω): Primary turns: N_p = 500 turns Secondary turns: N_s = N_p / 50 = 10 turns Actual turns ratio: 500:10 = 50:1. Z ratio = 50² = 2500:1. Z_in = 2500 × 8 = 20,000 Ω = 20 kΩ. ✓ TURNS RATIO N = 35:1 (Z_s = 10 kΩ → Z_L = 8 Ω): N_p = 350 turns, N_s = 10 turns. Z_in = (35)² × 8 = 9800 Ω ≈ 10 kΩ. ✓ WINDING WIRE SIZE: Primary (#1): #36–#38 AWG enameled (very fine; handle with care) For 500 turns on T-94A-77: use #36 AWG. Resistance ≈ 200–400 Ω (acceptable loss). Secondary (#2): #28–#30 AWG enameled For 10 turns: trivial. BIFILAR NOT suitable for this high-ratio transformer; use separate windings. ================================================================================ SCHEMATIC ================================================================================ CRYSTAL RADIO DETECTOR OUTPUT: AF (+) ─────────────────────────────────────── XFMR T1 PRIMARY (+) │ [N_p: 500 turns] │ GND ──────────────────────────────────────────── XFMR T1 PRIMARY (−) T1 SECONDARY: T1 SEC (+) ─── [headphone LEFT(+)] T1 SEC (−) ─── [headphone LEFT(−)] ─── GND For stereo (both channels): wire secondary in parallel or use two separate secondaries (bifilar secondary, 5+5 turns for stereo phones). FULL SCHEMATIC WITH RF FILTER: Tank output ─── [D1: 1N34A] ─────────────────────────── AF(+) │ [C_rf: 0.01µF] ← RF bypass BEFORE transformer │ GND AF(+) ──── [T1 primary: 500t] ──── GND (via primary DC path) │ [T1 secondary: 10t] │ [J2: 3.5mm jack, tip/ring to headphone] NOTE: T1 must not carry DC. Crystal radio detector output is pure AC audio (no DC component after RF bypass). Primary has no DC, so no DC saturation. IF using transformer with regenerative design (battery-powered): Add [C_dc: 10 µF electrolytic] in series with primary to block any residual DC. AF(+) ─── [C_dc: 10µF] ─── [T1 primary] ─── GND ================================================================================ WINDING PROCEDURE — TOROIDAL TRANSFORMER ================================================================================ CORE: Amidon T-94A-77 (24 × 14 × 10 mm) or equivalent Mix 77 toroid. STEP 1 — PREPARE CORE: Wrap core with 2 layers of electrical tape or heat-shrink tubing. This insulates the ferrite and protects fine wire. Mark start position with a small color dot (nail varnish or paint marker). STEP 2 — WIND SECONDARY (10 turns first, while core is empty): Use 15 cm of #28 AWG enameled wire. Pass wire through center, wrap around outside. Count each pass through the hole as one turn. 10 turns total. Mark start "S-" and end "S+". Twist ends lightly and fold out of the way against the core. Secure with tape. STEP 3 — WIND PRIMARY (500 turns): Use a 6 m length of #36 AWG enameled wire (= ~120 turns per meter). Wind in the SAME direction as secondary. Divide core into 4 quadrants; wind 125 turns per quadrant. Use a winding shuttle (small cardboard bobbin) to manage fine wire. After every 50 turns, count and record to avoid losing count. Mark start "P-" and end "P+". DO NOT break wire; count continuously. STEP 4 — STRIP AND TIN ENDS: Strip enamel from all 4 wire ends with fine sandpaper (400 grit). Tin with rosin-core solder. Test primary and secondary resistance: Primary (500t, #36 AWG): should read 150–400 Ω (depending on wire length) Secondary (10t, #28 AWG): should read < 1 Ω STEP 5 — TEST: Measure primary inductance with LC meter: Target: L_p ≥ 1 H at 400 Hz (for good low-frequency response) For T-94A-77: L = 900 nH × N² → for 500t: L = 900 nH × 250,000 = 225 H ✓ (Formula uses inductance factor A_L = 900 nH for T-94A-77) ALTERNATIVE QUICK TEST: Connect 9V battery through 1 kΩ to primary. Remove battery. Secondary should show brief voltage spike (transformer action). STEP 6 — EPOXY: Apply small drop of epoxy to secure wire ends to core. Do NOT pot entire transformer; difficult to diagnose if problems occur. ================================================================================ A_L INDUCTANCE FACTOR TABLE (for winding calculation) ================================================================================ For turns calculation: N = √(L_desired / A_L) Where L in µH and A_L in µH/N² (or equivalently nH/N²×1000). Core type A_L (µH/N²) L for 500 turns Notes --------- ----------- --------------- ----- T-94A-77 0.000900 225 H Best for audio; use this T-130-77 0.000197 49 H Smaller; marginal at LF T-50-77 0.000360 90 H Small; okay for 1kHz+ BN-73-302 0.000730 182 H Binocular; good choice Laminated (E-I) varies measure actual Salvage cores Permalloy tape 0.001500 375 H Excellent; expensive For minimum 1 H at 400 Hz: need A_L × N² ≥ 1 H = 1,000,000 µH. T-94A-77, N=500t: 0.0009 × 250,000 = 225 ✓ (225 H >> 1 H) T-50-77, N=500t: 0.00036 × 250,000 = 90 ✓ (marginal low-end response) A_L given in datasheet; check manufacturer for actual value. ================================================================================ INSERTION LOSS AND EFFICIENCY ================================================================================ TRANSFORMER LOSS SOURCES: 1. Primary winding resistance: R_p (copper loss) 2. Secondary winding resistance: R_s (copper loss) 3. Core hysteresis loss (audio frequencies; generally small with Mix 77) INSERTION LOSS CALCULATION: R_p = 350 Ω (typical, 500t #36 AWG on T-94A-77) R_s = 0.5 Ω (10t #28 AWG) R_s_reflected = R_s × N² = 0.5 × 2500 = 1250 Ω Total loss resistance: R_total = R_p + R_s_reflected = 350 + 1250 = 1600 Ω Source impedance: Z_s = 20,000 Ω Insertion loss: IL = 20 log(Z_s / (Z_s + R_total)) = 20 log(20000/21600) = −0.64 dB Efficiency: η = Z_s / (Z_s + R_total) = 20000/21600 = 92.6% Compared to 8 Ω directly across 20 kΩ source (without transformer): Power ratio: Z_L / Z_s = 8/20000 = 0.04% of available power (−34 dB loss) With transformer: 92.6% efficiency → +34 dB improvement in audio power. FREQUENCY RESPONSE: Low-frequency −3 dB: f_low = R_source / (2π × L_primary) R_source = detector Z ≈ 20 kΩ L_primary = 225 H (T-94A-77, 500t) f_low = 20,000 / (2π × 225) = 14 Hz (well below audio band ✓) High-frequency −3 dB: limited by leakage inductance and winding capacitance. Typical toroidal audio transformer: −3 dB at 15–50 kHz (well above 6 kHz needed ✓) Bandwidth for crystal radio audio: 300–3000 Hz (AM voice quality). This transformer is flat across 300–10,000 Hz with <1 dB variation. ================================================================================ ALTERNATE DESIGNS ================================================================================ DESIGN A — 11:1 RATIO (Z_s = 1 kΩ → 8 Ω): Use when source impedance is known to be 1 kΩ (e.g., high-Z magnetic earphone driven by high-Q tank directly). N_p = 110 turns, N_s = 10 turns. Wire: N_p #32 AWG, N_s #26 AWG. Core: T-94A-77 still works; or smaller T-68A-77. DESIGN B — 25:1 RATIO (Z_s = 5 kΩ → 8 Ω): N_p = 250 turns, N_s = 10 turns. General-purpose match for most crystal radios. Compromise: adequate for most designs. DESIGN C — AUDIO OUTPUT TRANSFORMER (SALVAGE): Old transistor radio audio output transformers (2-3W, primary ~2 kΩ, secondary 8 Ω) can be used directly. Primary will be ~200-300 turns, secondary 4-8 turns. Z ratio ≈ 200-300:1; too low for crystal radio (would need ~1000 Ω source). Usable with regenerative designs that have lower detector impedance. DESIGN D — E-I LAMINATED STEEL CORE (IF AVAILABLE): Classic salvage approach: use matching transformer from old AM/SW radio. These are designed exactly for crystal radio / detector impedances. Typical Z: 10 kΩ primary, 8 Ω secondary (ratio 35:1). No winding needed; just salvage and test. ================================================================================ COMPLETED TRANSFORMER SPECIFICATIONS ================================================================================ Parameter Value Notes --------- ----- ----- Primary turns 500 #36 AWG, T-94A-77 Secondary turns 10 #28 AWG Turns ratio 50:1 Actual: 500/10 Impedance ratio 2500:1 N² Primary impedance 20 kΩ at 8 Ω load Secondary impedance 8 Ω matched to headphone Primary inductance 225 H at 400 Hz, no load Primary resistance ~300 Ω DC; use lowest-resistance wire Secondary resistance < 1 Ω DC Insertion loss ~0.5 dB at Z_s=20kΩ Frequency response ±1 dB, 100–15 kHz flat Core T-94A-77 Mix 77 Amidon Dimensions (wound) ~35 × 20 mm core + windings Weight ~15 g without housing ================================================================================ PARTS LIST — HEADPHONE TRANSFORMER ================================================================================ Ref Qty Value/Part Description --- --- ---------- ----------- T1 1 see design above 500t/10t audio matching transformer — 1 T-94A-77 core Mix 77 ferrite toroid (Amidon) — 6m #36 AWG enameled Primary winding wire — 0.2m #28 AWG enameled Secondary winding wire — 1 electrical tape Core insulation C_dc 1 10 µF / 16V DC blocking cap (only for regen design) J2 1 3.5mm stereo jack Headphone output ================================================================================