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Amateurfunk-Anki/references/Hilfsmittel.md
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Hilfsmittel — official exam aid (Formelsammlung + tables)

Catalog of everything in the BNetzA exam aid sheet that candidates are allowed to use during the exam, with the printed page numbers as they appear on each page. This file is the source of truth for the <u>Hilfsmittel:</u> notes appended to explanations (see EXPLANATIONS.md): a note may only cite a formula/table that is listed here, and should name it and its page.

If the fact a question needs is not in this list (e.g. diode forward voltages ~0.6 V / ~0.3 V, tan δ = 1/Q, semiconductor behaviour, definitions), it is a memory item — do not add a Hilfsmittel note.

S. 1–3 — Frequenzbereichszuweisung (Anlage 1, Amateurfunkverordnung)

  • S. 1 — Nutzungsbedingungen (¶1–4): general usage rules (incl. the 50 W ERP cap for remote/automatic terrestrial stations above 30 MHz, with a possible 1000 W ERP exception for links) and, in ¶3, the definitions of a primärer and sekundärer Funkdienst and their protection/priority rights. This is a text page, not a table. (No 750 W figure appears here — 750 W PEP is a class-A limit in the S. 2 table.)
  • S. 2 — Tabellarische Übersicht: per frequency band: status (primary/secondary), the allowed frequency ranges, max. power per licence class (A/E/N) — in PEP or ERP exactly as printed (not EIRP), and additional-usage references. Note the units: class N on 10 m is 10 W ERP, but on 2 m/70 cm it is 6,1 W ERP (= ≈10 W EIRP after ×1,64, see S. 15) — the table does not print "10 W EIRP". Power limits are in PEP/ERP, never EIRP.
  • S. 3 — Zusätzliche Nutzungsbestimmungen (numbered conditions): max. occupied bandwidth per band (800 Hz, 2,7 kHz, 7 kHz, 40 kHz, 2 MHz …), and special power limits such as the 1247–1263 MHz 3,05 W ERP sub-band cap (= ≈5 W EIRP). The bandwidth values live in these numbered conditions, not in the S. 2 table.

Not in Anlage 1: the general HF/VHF/UHF (KW/UKW) range terminology, the ISM-band definition, and foreign-country prefixes (Landeskenner) — those are memory items.

S. 4–7 — Rufzeichenplan für den Amateurfunkdienst in Deutschland

  • S. 4 — intro: structure of German call signs (prefix DA–DR excl. DE/DI, digit, 2–3-char suffix).
  • S. 5 — Tabelle "Rufzeichen mit 2- oder 3-buchstabigen Suffixen": the main call-sign-series → class/use table. DA0 = Klubstation; DL1–DL9 = person-bound class A; DO1–DO9 = class E; DN9 = class N; DP0–DP1 = exterritorial class A; etc.
  • S. 6 — club-station suffixes (1-char) table.
  • S. 7 — club-station suffixes (4–7-digit); § 5 Kurzzeitzulassungen ausländischer Funkamateure (visitors in Germany sign DL/ class A, DO/ class E); § 6 Kennungen zum Betrieb leistungsschwacher Sender (beacon/peil identifiers MO, MOE, MOI, MOS, MOH, MO5); §§ 7–8 rules.

S. 8 — International gebräuchliche Rufzeichenzusätze / Ausbildung / Remote

  • § 9 operating suffixes appended with /: /m (mobile, incl. inland-waterway), /mm (maritime mobile), /am (aeronautical mobile), /p (portable/temporary fixed; optional in Germany), etc.
  • § 10 Ausbildungsfunkbetrieb (/Trainee speech, /T CW/digital).
  • § 11 Remotebetrieb (Remote speech, /R CW/digital).

Foreign-country prefixes (e.g. Swiss HB3/HB9 for a German operating abroad) are not in this plan — memory item.

S. 9–10 — IARU-Bandplan

  • S. 9 — 2 m and S. 10 — 70 cm: per segment, max bandwidth, preferred mode and usage (CW, SSB, FM, digital, beacons, satellite…).

S. 11 — Formelsammlung: Grundlagen / Widerstände

  • Zehnerpotenzen & SI-Präfixe (p…T) — table.
  • Zweierpotenzen / Bit (2^0…2^12) — table.
  • Ohmsches Gesetz: U = R·I, R = U/I, I = U/R.
  • Innenwiderstand: R_i = ΔU/ΔI.
  • Widerstand von Drähten: R = ρ·l/A_Dr, A_Dr = d²·π/4 = r²·π.
  • Widerstands-Farbcode — table (Farbe / Wert / Multiplikator / Toleranz).

S. 12 — Widerstandsnetzwerke / Leistung / Wechselspannung

  • Reihenschaltung: R_G = R1+R2+…+R_N; 2 R: R_G = R1+R2.
  • Parallelschaltung: 1/R_G = 1/R1+1/R2+…; 2 R: R_G = R1·R2/(R1+R2).
  • Spannungsteiler (unbelastet): U_G = U1+U2, U1/U2 = R1/R2, U2/U_G = R2/(R1+R2).
  • Stromteiler: I_G = I1+I2, I2/I1 = R1/R2.
  • Vorzugsreihen E6/E12/E24 — table.
  • Leistung: P = U·I = U²/R = I²·R; U = P/I = √(P·R); I = P/U = √(P/R).
  • Arbeit/Energie: W = P·t.
  • Wirkungsgrad: η = P_ab/P_zu (·100 %); P_ab = P_zu − P_V.
  • Wechselspannung: Û = U_eff·√2, U_SS = 2·Û, ω = 2·π·f, Z = √(R²+X²), T = 1/f, f = 1/T.

S. 13 — Induktivität / Transformator / Kapazität

  • Induktiver Blindwiderstand: X_L = ω·L.
  • L Reihe: L_G = L1+…+L_N; L Parallel: 1/L_G = 1/L1+….
  • Ringspule / lange Zylinderspule: L = μ0·μr·N²·A_S / l(_m).
  • Ringkernspulen (auch mehrlagig): L = N²·A_L.
  • Magnetische Feldstärke (Ringspule): H = I·N/l_m.
  • Magnetische Flussdichte: B_m = μr·μ0·H.
  • Transformator-Übersetzungsverhältnis: ü = N_P/N_S = U_P/U_S = I_S/I_P = √(Z_P/Z_S).
  • Belastbarkeit von Wicklungen: I = S·A_Dr mit S ≈ 2,5 A/mm².
  • Kapazitiver Blindwiderstand: X_C = 1/(ω·C).
  • C Reihe: 1/C_G = 1/C1+…; C Parallel: C_G = C1+….
  • E-Feld im homogenen Feld: E = U/d.
  • Kapazität Kondensator: C = ε0·εr·A/d.

S. 14 — Filter / Schwingkreis / Transistor / ZF & Spiegelfrequenz

  • RC TP/HP: f_g = 1/(2π·R·C); RL TP/HP: f_g = R/(2π·L) (f_g = −3 dB-Grenzfrequenz).
  • Schwingkreis: f0 = 1/(2π·√(L·C)), Resonanz X_C = X_L.
  • Reihenschwingkreis: B = R_s/(2π·L), Q = f0/B = X_L/R_s.
  • Parallelschwingkreis: B = 1/(2π·R_p·C), Q = f0/B = R_p/X_L.
  • Transistor (DC): B = I_C/I_B, I_E = I_C+I_B.
  • Transistor (AC): v_I = β = ΔI_C/ΔI_B, v_U = β = ΔU_CE/ΔU_BE, v_P = β² = v_U·v_I. (Transcribed verbatim. The printed v_U = β is physically dubious — voltage gain is not generally the current gain — but the aid prints it this way; do not silently "correct" it.)
  • Zwischenfrequenz: f_ZF = |f_E − f_OSZ| (the sheet notes that the f_ZF = f_E + f_OSZ case is not considered).
  • Spiegelfrequenz: f_S = 2·f_OSZ − f_E.

S. 15 — Pegel / Antennen

  • Pegel: p = 10·log10(P/1mW) dBm; p = 10·log10(P/1W) dBW; u = 20·log10(U/0,775V) dBu.
  • Verstärkung/Gewinn: g = 10·log10(P2/P1) dB; g = 20·log10(U2/U1) dB.
  • Dämpfung/Verluste: a = 10·log10(P1/P2); a = 20·log10(U1/U2).
  • dB ↔ Verhältnis-Tabelle — exactly 11 rows (Leistungs- / Spannungsverhältnis): −20 (0,01/0,1), −10 (0,1/0,32), −6 (0,25/0,5), −3 (0,5/0,71), −1 (0,79/0,89), 0 (1/1), +1 (1,26/1,12), +3 (2/1,41), +6 (4/2), +10 (10/3,16), +20 (100/10). There is no 16 dB row (or any value off this list): combine rows, e.g. 16 dB = +10 dB (×10) + +6 dB (×4) → ×40.
  • ERP: p_ERP = p_S − a + g_d; P_ERP = P_S·10^((g_d−a)/10dB).
  • EIRP: p_EIRP = p_ERP + 2,15 dB; P_EIRP = P_ERP·1,64.
  • Feldstärke Fernfeld: E = √(30Ω·P_A·G_i)/d = √(30Ω·P_EIRP)/d (ab d > λ/(2π)).
  • Gewinn: G_i = G_d·1,64, g_i = g_d + 2,15 dB, G = 10^(g/10dB).
  • Halbwellendipol G_i=1,64 / g_i=2,15 dB; λ/4-Vertikal mit Bodenreflexion G_i=3,28 / g_i=5,15 dB; Parabolspiegel g_i = 10·log10[(π·d/λ)²·η] dB.

S. 16 — Rauschen / Amplitudenmodulation / Frequenzmodulation

  • Thermisches Rauschen: P_R = k·T_K·B; Δp_R = 10·log10(B1/B2); U_R = 2·√(P_R·R).
  • Rauschzahl: F = (P_S/P_N)_Eingang/(P_S/P_N)_Ausgang; a_F = 10·log10(F); a_F = SNR_Eingang − SNR_Ausgang.
  • SNR: SNR = 10·log10(P_S/P_N) = 20·log10(U_S/U_N).
  • Shannon-Hartley: C = B/1Hz · log2(1 + P_S/P_N) bit/s.
  • log2: log2(x) = log10(x)/log10(2).
  • AM Modulationsgrad: m = Û_mod/Û_T; AM Bandbreite: B = 2·f_mod,max.
  • FM Modulationsindex: m = Δf_T/f_mod; Carson-Bandbreite: B ≈ 2·(Δf_T + f_mod,max).

S. 17 — Wellenlänge & Frequenz / Reflexion / Wellenwiderstand

  • c = f·λ, f = c/λ, λ = c/f; c0 ≈ 3·10⁸ m/s; f[MHz] ≈ 300/λ[m], λ[m] ≈ 300/f[MHz].
  • Verkürzungsfaktor: k_v = l_G/l_E = 1/√εr = c/c0.
  • Stehwellenverhältnis (SWR): s = U_max/U_min = (U_v+U_r)/(U_v−U_r) = (√P_v+√P_r)/(√P_v−√P_r) = (1+|r|)/(1−|r|); s = R2/Z (R2>Z) bzw. s = Z/R2 (R2<Z).
  • Reflexionsfaktor: |r| = (s−1)/(s+1) = |(R2−Z)/(R2+Z)| = |U_r/U_v| = √(P_r/P_v).
  • Rücklaufende Leistung: P_r = P_v·|r|².
  • An R2 abgegebene Leistung: P_ab = P_v·(1−|r|²).
  • Wellenwiderstand: HF-Leitung Z = √(L'/C'); Koax Z = 60Ω/√εr·ln(D/d); symm. Zweidraht (a/d>2,5) Z = 120Ω/√εr·ln(2a/d); Viertelwellentransformator Z = √(Z_E·Z_A).

S. 18 — Weitere Formeln

  • MUF: MUF ≈ f_c/sin(α); f_opt = MUF·0,85.
  • Empfindlichkeit von Messsystemen: E_MESS = R_i/U_i = 1/I_i.
  • Relativer maximaler Fehler: F_W = ±(G/100)·(W_E/W_M).
  • Abtasttheorem: f_abtast > 2·f_max; für Nicht-Basisband-Signale f_abtast > 2·(f_max − f_min) wenn f_abtast < f_min oder f_abtast > f_max.
  • Datenübertragungs-/Symbolrate: C = R_S·n.

S. 19–22 — Konstanten und Tabellen

  • S. 19–20 — symbol/quantity glossary and physical constants (k, c0, μ0, ε0, e, …).
  • S. 21 — material tables: relative permittivity ε_r and specific resistance ρ (per the S. 21 erratum, Zink → Zinn).
  • S. 22 — Kabeldämpfungsdiagramm Koaxialkabel: a chart of cable attenuation in dB per 100 m vs. frequency for common coax types (RG58 ≈ 4,95 mm, RG174 ≈ 2,8 mm, PE-foam 10,3/12,7 mm, …). Read the per-100 m loss at the operating frequency, then scale linearly with cable length. This chart is part of the aid — cable-loss questions are Hilfsmittel lookups.
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