Dipole Antenna Length Calculator
Formula
The classic half-wave dipole formula accounts for the fact that a real wire antenna resonates slightly shorter than a theoretical half-wavelength due to end effects and wire diameter:
Total length (ft) = 468 / f(MHz) × VF
Each leg = total / 2. To convert to meters, multiply feet by 0.3048.
Assumptions
- The constant 468 (instead of the theoretical 492 = 984/2) accounts for typical wire end effects.
- Default velocity factor of 0.95 is appropriate for bare copper or aluminum wire in free space.
- This formula assumes a center-fed dipole in free space. Height above ground, nearby objects, and feed line interactions will shift the actual resonant frequency.
- For tubing elements (Yagi, beam), use a lower VF (~0.96–0.98). For thick tubing, end-effect correction is less pronounced.
Tips & Tricks
- Cut slightly long (add 2–3%) and trim to resonance with an antenna analyzer.
- A dipole fed with 50Ω coax will present roughly 72Ω at resonance in free space — SWR around 1.4:1 is normal.
- Lowering a dipole closer to ground raises its feed impedance. At 0.1λ height, impedance can drop to 25–35Ω.
- Multiband operation: a 40m dipole also resonates on 15m (3rd harmonic). Use a 1:1 current balun to reduce feedline radiation.
Vertical Antenna Length Calculator
Formula
Length = (300 / f) × fraction × VF
Where fraction is 0.25 for 1/4-wave, 0.5 for 1/2-wave, etc. Free-space wavelength = 300/f(MHz) meters.
Assumptions
- Assumes a vertical monopole over a perfect ground plane.
- A 1/4-wave vertical over a good ground presents ~36Ω radiation resistance. With ground losses, effective feed impedance is typically 50–52Ω.
- The 5/8-wave vertical has higher gain (~3 dBi) than a 1/4-wave but requires a matching network to bring the feed impedance down to 50Ω.
Tips & Tricks
- Ground radials are critical. Four λ/4 radials will get you most of the way there; 16–32 radials approach a perfect ground.
- Elevated radials (at least 4, tuned to λ/4) can outperform many buried radial systems.
- A 1/2-wave vertical requires no ground plane and presents high impedance at the feed — use a matching transformer or feed it with 300Ω ladder line.
- At HF, soil conductivity varies widely. Sandy soil is a poor ground; salt marshes are excellent.
Yagi Element Length & Spacing Calculator
Formula
Uses W1JR optimized proportions as a fraction of free-space wavelength (λ = 300/f meters):
Reflector : 0.500 × λ
Driven el. : 0.473 × λ
Director 1 : 0.440 × λ
Director 2 : 0.430 × λ
Director 3 : 0.422 × λ
Spacing (from driven):
Reflector : −0.200 × λ
Director 1 : +0.125 × λ
Director 2 : +0.250 × λ
Director 3 : +0.375 × λ
Assumptions
- These are starting proportions for thin elements (diameter << λ). Thick tubing or large-diameter elements require correction.
- Gain estimates (5–10 dBi) are approximate; actual gain depends on element taper, boom diameter, and matching network.
- The driven element is assumed to be a split dipole with a direct 50Ω feed via a gamma or beta match.
Tips & Tricks
- Boom correction: conductive booms detune elements. Shorten elements by ~1% when mounted on a metal boom.
- For VHF/UHF, element diameter becomes significant. Use EZNEC or YO (Yagi Optimizer) to model your specific element diameter.
- Stacking two Yagis vertically with ~λ spacing yields ~3 dB additional gain.
- F/B (front-to-back) ratio is very sensitive to reflector length. Tune the reflector for best F/B, not best SWR.
Inverted V Antenna Calculator
Formula
Total wire = 468 / f(MHz) (ft)
Each leg = total / 2
Half-span = leg × cos(apex_angle / 2)
Assumptions
- Uses the same 468 constant as a flat dipole; in practice an inverted V resonates slightly longer due to the angle, so expect to trim slightly.
- Feed impedance decreases as the apex angle narrows. At 90° it is approximately 50Ω; at 120° closer to 72Ω.
- End height above ground is not accounted for but significantly affects radiation pattern and impedance.
Tips & Tricks
- An apex angle of 90–120° gives a good compromise between height requirement and feed impedance close to 50Ω.
- The inverted V has a more omnidirectional pattern than a flat dipole, making it popular for general HF use.
- Ends should be at least 1–2 meters above ground to avoid RF contact hazards and detuning from the earth.
- Using a 1:1 current balun at the feed point reduces common-mode current on the coax shield.
Simple Antenna Gain Calculator
Formula
Radiated power = Pfwd − Pref
Γ = sqrt(Pref / Pfwd)
SWR = (1 + Γ) / (1 − Γ)
Total gain (dBi) = Reference gain (dBi) + measured delta (dB)
ERP = Radiated power × 10^(gain_dBi / 10)
Assumptions
- Reference gain of 2.15 dBi is the gain of a half-wave dipole in free space, the standard reference for dBd conversion.
- dBd = dBi − 2.15. A 0 dBd antenna has the same gain as a reference dipole.
- ERP (Effective Radiated Power) does not account for feed line loss between the transmitter and antenna.
Tips & Tricks
- To measure antenna gain, compare received signal strength against a reference dipole at the same height and orientation.
- FCC licensing often specifies power limits in ERP or EIRP (isotropic). EIRP = ERP + 2.15 dB.
- Keep SWR below 2:1 at the transmitter to avoid PA stress; most solid-state rigs fold back power above SWR 2:1–3:1.
Loading Coil Calculator (Shortened Antennas)
Formula
For a base-loaded monopole shorter than λ/4, the required inductive reactance to resonate the antenna is:
Electrical angle θ = (physical_length / quarter_wave_length) × 90°
Required Xl = Rr / tan(θ)
Required L (µH) = Xl / (2πf)
Assumptions
- Base loading (coil at the bottom) is the most common but least efficient position — the coil is in a region of low current.
- Center loading (coil at mid-height) improves efficiency because the coil sits in a higher-current region.
- The radiation resistance Rr decreases sharply as the antenna is shortened. At 50% of λ/4, Rr may be only 5–10Ω, making ground losses dominant.
- Assumes a linear current distribution, which is an approximation for very short antennas.
Tips & Tricks
- Wind the loading coil with heavy gauge wire (14 AWG or heavier) to minimize coil resistance and maximize Q.
- High-Q coils (air-wound, silver-plated) can significantly improve efficiency. Commercial mobile whips often use poor Q coils to reduce cost.
- A capacity hat (horizontal spokes at the top) reduces the required inductance and raises efficiency.
- For mobile HF antennas, even a well-designed loading coil antenna may be 10–20 dB below a full-size antenna on 80m/40m.
Antenna Tuner Matching Calculator
Formula
Z ratio = ZL / ZS
SWR = max(ZL, ZS) / min(ZL, ZS) (resistive loads only)
Return loss = −20 × log10(|Γ|)
Γ = (ZL − ZS) / (ZL + ZS)
Network Q ≈ sqrt(max_ratio − 1)
Assumptions
- This calculator treats impedances as purely resistive. Real antenna impedances have reactive components (jX) that also require matching.
- The Q estimate reflects the minimum Q needed to achieve the transformation ratio with an L-network. Pi and T networks allow you to set Q independently.
Tips & Tricks
- Use the Pi-Network calculator for tube PA output tanks — higher Q provides better harmonic suppression.
- A tuner at the transmitter only improves the transmitter's SWR — it does not reduce feed line loss caused by high SWR on the line itself. Place the tuner at the antenna feed point for best efficiency.
- Ladder line (300Ω or 450Ω) tolerates very high SWR with low loss, making it ideal for multiband antennas fed with a balanced tuner.
Frequency ↔ Wavelength Calculator
Formula
λ (meters) = c / f = 300 / f(MHz)
f (MHz) = 300 / λ (meters)
Speed of light c = 299,792,458 m/s ≈ 300 × 10&sup6; m/s. The approximation 300/f is accurate to 0.07%.
Tips & Tricks
- In free space. Wavelength inside a transmission line or antenna element is shorter by the velocity factor.
- Quick mental math: 300m at 1 MHz, 30m at 10 MHz, 3m at 100 MHz, 30cm at 1 GHz.
- Ham bands in wavelength terms: 160m, 80m, 40m, 30m, 20m, 17m, 15m, 12m, 10m, 6m, 2m, 70cm, 23cm.
Ohm's Law Calculator
Formulas
E = I × R (Voltage = Current × Resistance)
I = E / R (Current = Voltage / Resistance)
R = E / I (Resistance = Voltage / Current)
P = E × I (Power = Voltage × Current)
P = I² × R (Power = Current² × Resistance)
P = E² / R (Power = Voltage² / Resistance)
Tips & Tricks
- Enter any two known values and leave the others blank. The calculator will solve for the remaining two.
- For RF circuits, R is the real part of impedance (resistance). Reactive components (L, C) do not dissipate power but do affect current and voltage.
- A 100W transmitter into 50Ω: E = sqrt(100 × 50) = 70.7V RMS, I = sqrt(100/50) = 1.41A RMS.
- Dummy loads dissipate all power as heat: P = E²/R. A 100W load into 50Ω needs to handle 70.7V peaks RMS.
Decibel Calculator
Formulas
Power ratio → dB : dB = 10 × log10(P2/P1)
Voltage ratio → dB : dB = 20 × log10(V2/V1)
dBm = 10 × log10(P_mW) [ref: 1 milliwatt]
dBW = 10 × log10(P_W) [ref: 1 watt]
Key Reference Points
- +3 dB ≈ 2× power; −3 dB ≈ half power
- +10 dB = 10× power; −10 dB = 0.1× power
- +6 dB ≈ 2× voltage (4× power into same impedance)
- 0 dBm = 1 mW; +30 dBm = 1 W; +60 dBm = 1 kW
- 100W = +50 dBm; 1500W (legal limit) = +61.8 dBm
Tips & Tricks
- dB is always a ratio. dBm and dBW are absolute power levels referenced to a known quantity.
- Use power dB (factor 10) for power gain/loss; use voltage dB (factor 20) when comparing voltages into the same impedance.
- System gain/loss chains: just add the dB values. 100W TX − 3dB coax loss + 6dB antenna gain = 103W ERP.
Resistor Color Code Calculator (4-Band)
Band Decoding
Value = (Band1 × 10 + Band2) × Multiplier
Min = Value × (1 − Tolerance/100)
Max = Value × (1 + Tolerance/100)
Color to Digit Reference
- Black=0, Brown=1, Red=2, Orange=3, Yellow=4
- Green=5, Blue=6, Violet=7, Gray=8, White=9
- Gold multiplier = ×0.1, Silver = ×0.01
- Gold tolerance = ±5%, Silver = ±10%
Tips & Tricks
- Mnemonic: Black Bears Robbed Our Yard, Great Big Vicious Grizzly Wolves.
- 5-band resistors add a third significant digit and use brown/red/green/blue/violet for 1%/2%/0.5%/0.25%/0.1% tolerance.
- For RF circuits, use metal film resistors (±1%) rather than carbon composition for better stability and lower noise.
- At VHF and above, resistor lead length becomes significant. Use surface-mount components to minimize parasitic inductance.
Capacitor / LC Resonance Calculator
Formulas
Resonant frequency: f = 1 / (2π × sqrt(L × C))
Find C for resonance: C = 1 / ((2πf)² × L)
Capacitive reactance: Xc = 1 / (2πf × C)
Tips & Tricks
- Units: L in henries, C in farads for the raw formula. The calculator handles µH and pF conversions automatically.
- Inductive reactance: Xl = 2πf × L. At resonance, Xl = Xc and they cancel, leaving only the resistive loss.
- Tank circuit Q = Xl / R (series) or R / Xl (parallel). Higher Q = sharper filter response and more selectivity.
- For transmitter tank circuits, choose C values that give reasonable voltage ratings. At 100W into 50Ω, peak tank voltage can exceed several hundred volts.
- Ceramic capacitors have poor temperature stability (especially Y5V/Z5U). Use NP0/C0G or silver mica for RF frequency-determining circuits.
Battery Life Calculator
Formula
Avg current = (I_TX × TX%) + (I_RX × (1 − TX%))
Battery life (hrs) = Capacity (mAh) / Avg current (mA)
Assumptions
- Assumes constant TX and RX current draw and a fixed duty cycle. Real operation varies widely.
- Battery capacity is derated in practice: cold temperatures, age, and discharge rate all reduce effective capacity.
- Peukert's effect: high-current draws (such as a 100W HF rig) extract less total energy than a slow trickle discharge would suggest.
Tips & Tricks
- For SSB voice, 50% TX duty cycle is a reasonable estimate (talk/listen ratio). For FT8, TX cycles are exactly 50% (15 seconds on/off).
- A 100Ah AGM battery at 12V can theoretically supply 100A for 1 hour — but in practice derate by 20–30% for usable capacity before voltage sags.
- LiFePO4 batteries are nearly flat in discharge voltage down to ~20% SOC, making them ideal for field portable operation.
- Include voltage regulator and display standby draw in your RX current estimate for digital modes rigs.
SWR (Standing Wave Ratio) Calculator
Formulas
From power: Γ = sqrt(Pref / Pfwd)
From impedance: Γ = |ZL − Z0| / |ZL + Z0|
SWR = (1 + |Γ|) / (1 − |Γ|)
Return loss = −20 × log10(|Γ|) dB
Mismatch loss = −10 × log10(1 − |Γ|²) dB
SWR Reference Table
- SWR 1.0:1 — perfect match, 0% reflected power
- SWR 1.5:1 — 4% reflected, 0.18 dB mismatch loss
- SWR 2.0:1 — 11% reflected, 0.51 dB mismatch loss
- SWR 3.0:1 — 25% reflected, 1.25 dB mismatch loss
- SWR 5.0:1 — 44% reflected, 2.55 dB mismatch loss
Tips & Tricks
- SWR measured at the transmitter includes feed line loss — high-loss cable can mask a badly mismatched antenna by absorbing the reflected wave.
- Most modern solid-state rigs begin power fold-back at SWR 2:1–3:1. This protects the PA but reduces output.
- Tube rigs tolerate higher SWR at the PA output, but the antenna tuner should still be adjusted for minimum SWR on the feed line.
VSWR ↔ Return Loss Converter
Formulas
Γ = (VSWR − 1) / (VSWR + 1)
Return loss (dB) = −20 × log10(Γ)
VSWR = (1 + Γ) / (1 − Γ)
where Γ = 10^(−RL_dB / 20)
Tips & Tricks
- Return loss is used more commonly in microwave engineering; VSWR dominates HF/VHF amateur practice.
- A return loss of 14 dB corresponds to SWR 1.5:1, which is considered acceptable for most amateur use.
- 20 dB return loss (SWR 1.22:1) is considered excellent. Commercial systems often specify 20–30 dB.
- Use return loss notation when working with spectrum analyzers and directional couplers — it is easier to read directly in dB.
Voltage Divider Calculator
Formula
Vout = Vin × R2 / (R1 + R2)
Idle current = Vin / (R1 + R2)
Attenuation = 20 × log10(Vout / Vin) dB
Tips & Tricks
- For a resistive voltage divider to work reliably, the load impedance should be at least 10× the value of R2 (stiff divider rule).
- RF attenuator pads (L, T, π) are designed to maintain a specific impedance on both ports — use the Pi/T network calculators for those.
- For biasing purposes in transistor circuits, choose R1 and R2 so that the bleed current (idle current) is 5–10× the expected base current.
Coax Loss Calculator
Formula
Loss (dB) = k × (length / 100) × sqrt(f / 100)
where k = manufacturer's loss constant (dB/100ft at 100 MHz)
The sqrt(f) scaling reflects the dominant skin-effect loss mechanism, which increases with the square root of frequency.
Assumptions
- Loss constants are for a matched load (SWR 1:1). With high SWR, additional loss occurs because current peaks in the line are higher.
- Temperature affects loss slightly; the constants are for typical ambient conditions.
- Connectors add approximately 0.1–0.3 dB each at UHF frequencies. Don't ignore connector loss in long runs.
Quick Reference (100 ft at 146 MHz)
- RG-58: ~5.3 dB loss (only 30% of power reaches antenna)
- RG-8/213: ~2.1 dB loss (62% reaches antenna)
- LMR-400: ~1.4 dB loss (73% reaches antenna)
- LMR-600: ~0.9 dB loss (81% reaches antenna)
Tip: Upgrade to larger coax before buying a bigger amplifier. Going from RG-58 to LMR-400 on 100ft at 2m recovers nearly 4 dB — equivalent to 2.5× the transmit power.
L-Network Impedance Matching Calculator
Formula
Q = sqrt(Rs / RL − 1)
Shunt reactance Xp = Rs / Q (across high-Z port)
Series reactance Xs = Q × RL (in series with low-Z port)
Xp → C = 1/(2πf × Xp)
Xs → L = Xs / (2πf)
Assumptions
- Rs must be greater than RL. The L-network always steps impedance down from the shunt-arm port to the series-arm port.
- The Q is fixed by the impedance ratio — you cannot choose it independently (unlike Pi or T networks).
- A low-pass L-network uses a shunt C and series L. A high-pass version (shunt L, series C) also exists.
Tips & Tricks
- L-networks have only two reactive elements, making them simpler to build than Pi or T networks.
- Because Q is set by the ratio, a large impedance transformation ratio forces a high Q and narrow bandwidth.
- For broadband amplifier output matching, cascaded L-sections are used to achieve wideband performance at a more moderate Q per section.
Pi-Network Impedance Matching Calculator
Formula
Virtual RL_eff = Rin × (Q² + 1)
Qout = sqrt(RL_eff / Rout − 1)
C1 = 1 / (2πf × Rin/Q)
L = Rin × Q / (2πf)
C2 = 1 / (2πf × Rout/Qout)
Assumptions & Notes
- The Pi-network is the classic tube amplifier output circuit. Rout is typically the plate impedance (~1000–5000Ω), Rin is the antenna/load impedance (50–75Ω).
- Higher Q means better harmonic suppression but narrower bandwidth.
- Q of 10–15 is typical for HF tube PA tanks; provides good harmonic rejection.
- The Pi-network acts as a low-pass filter — it inherently attenuates harmonics.
Tips & Tricks
- For variable tuning, C1 and C2 are usually variable capacitors. The inductor is tapped or switched for band changes.
- Capacitor voltage ratings must account for peak RF voltage. At 1500W into 50Ω, peak voltage is ~387V; in a high-Q tank the capacitor voltage can be much higher.
T-Network Impedance Matching Calculator
Formula
Xl1 = Rin × Q
RL_virtual = Rin × (Q² + 1)
Qout = sqrt(RL_virtual / Rout − 1)
Xl2 = Rout × Qout
Xc_shunt = RL_virtual / (Q + Qout)
L1 = Xl1 / (2πf)
L2 = Xl2 / (2πf)
C = 1 / (2πf × Xc_shunt)
Notes
- The T-network is common in antenna tuners because both series arms are inductors, which are easier to implement with roller inductors or switched coils.
- Unlike the Pi, the T-network is a high-pass topology, which means it provides less harmonic attenuation from the transmitter.
- The T-network can match a wider range of impedances than the L-network and allows Q selection.
Tip: The T-network's high-pass characteristic can actually amplify harmonic content relative to the fundamental if not carefully designed. Follow a T-tuner with a low-pass filter for transmitting applications.
Smith Chart Plotter
How to Read a Smith Chart
The Smith Chart maps complex reflection coefficients (Γ) onto a circle of unit radius. Any passive impedance Z = R + jX maps to a unique point inside or on the unit circle.
- Center: Perfect match (Z = Z0, Γ = 0, SWR = 1:1)
- Left edge: Short circuit (Z = 0, Γ = −1)
- Right edge: Open circuit (Z = ∞, Γ = +1)
- Upper half: Inductive impedances (positive X)
- Lower half: Capacitive impedances (negative X)
- Circles through center: Constant resistance (R)
- Arcs tangent to right edge: Constant reactance (X)
Formula Used
Γ = (Z − Z0) / (Z + Z0)
where Z = R + jX and Z0 is the reference impedance
Γ_r = (R² + X² − Z0²) / ((R+Z0)² + X²)
Γ_i = 2 × X × Z0 / ((R+Z0)² + X²)
Tips & Tricks
- Moving along a constant-SWR circle (concentric dashed circle) represents adding transmission line length.
- Adding a series inductor moves a point clockwise up along a constant-R circle.
- Adding a shunt capacitor moves a point clockwise up along a constant-G (conductance) arc.
- Use the chart to visualize matching networks: start at your load point and plot the component transformations to reach the center.
- The Z0 field changes the normalization. Set it to match your system impedance (typically 50Ω).
Balun / Unun Impedance Ratio Calculator
Formula
Impedance ratio = Zout / Zin
Turns ratio n = sqrt(Zout / Zin)
Ruthroff Zo = sqrt(Zin × Zout)
Balun vs. Unun
- Balun (BALanced to UNbalanced): converts between a balanced line (e.g., dipole) and unbalanced line (e.g., coax). Common types: 1:1, 4:1.
- Unun (UNbalanced to UNbalanced): transforms impedance without changing balance. Common: 4:1, 9:1 for end-fed antennas.
Standard Ratios
- 1:1 — Isolation/common-mode choke only. No impedance transformation.
- 4:1 — 200Ω → 50Ω. Used for G5RV, folded dipole, W8JK arrays.
- 9:1 — 450Ω → 50Ω. Used for end-fed half-wave (EFHW) antennas.
- 16:1, 25:1 — Very high impedance loads such as Beverage antennas and long wires.
Tips & Tricks
- The most important function of a 1:1 balun at a dipole feedpoint is choking common-mode current, not impedance transformation.
- Ferrite core material matters: Mix 43 (Fair-Rite) is good for HF choke baluns; Mix 61 for broadband transformers above 10 MHz.
- Check balun core saturation when running high power. Ferrite cores can saturate and heat up, destroying the balun.
Quarter-Wave Transformer Calculator
Formula
Zt = sqrt(Z1 × Z2)
Physical length = (λ/4) × VF = (300 / f / 4) × VF meters
How It Works
A transmission line section that is exactly λ/4 long transforms impedance by the square relationship above. This is because the input impedance of a shorted λ/4 line is infinite, and an open λ/4 line appears as a short.
Tips & Tricks
- A λ/4 transformer is frequency-specific — it only transforms correctly at the design frequency and odd harmonics.
- To match 50Ω to 75Ω: Zt = sqrt(50×75) = 61.2Ω. RG-59 (75Ω) in series with a section of RG-58 can approximate this.
- For broadband matching, use tapered transmission lines or cascaded transformers.
- Hairpin matches and beta matches on Yagi antennas are implementations of λ/4 transformer principles.
Complex Impedance Calculator (R + jX)
Operations
Series: Z = (R1+R2) + j(X1+X2)
Parallel: Z = (Z1×Z2)/(Z1+Z2) [complex division]
SWR: Γ = (ZL−Z0)/(ZL+Z0), SWR = (1+|Γ|)/(1−|Γ|)
Magnitude: |Z| = sqrt(R² + X²), angle = atan2(X, R)
Sign Convention
- Positive X (jX > 0): inductive reactance. The impedance looks like a coil.
- Negative X (jX < 0): capacitive reactance. The impedance looks like a capacitor.
- At resonance: X = 0, the impedance is purely resistive.
Tips & Tricks
- To cancel a reactive component: add an equal and opposite reactance in series. If Z = 50 − j30, add +j30 (a series inductor of Xl=30Ω) to resonate.
- For the SWR mode, enter Z0 (system impedance) in Z1 and the load impedance in Z2.
Velocity Factor Calculator
Formula
VF = measured_length / calculated_free_space_length
Physical length = free_space_length × VF
What is Velocity Factor?
The velocity factor is the ratio of the speed of an electromagnetic wave in a medium (cable, wire) to the speed of light in free space. A VF of 0.66 means signals travel at 66% of c through that cable.
Typical Velocity Factors
- Bare wire in free space: ~0.95–0.98
- RG-58 / RG-8 (solid PE): 0.66
- RG-8X / foam PE: 0.78–0.82
- LMR-400: 0.85
- Open wire / ladder line: 0.95–0.98
- Twin lead 300Ω: 0.82
Tips & Tricks
- Measure VF with an antenna analyzer: connect a short at the far end of a cable and find the frequency where it reads as a short (full λ/2 line). VF = measured_length / (150/f).
- Cable VF can vary ±2% from the nominal value, even within the same reel. Measure critical phasing lines.
Coaxial Cable Quarter-Wave Length
Formula
Quarter-wave length = (300 / f / 4) × VF meters
= (984 / f / 4) × VF feet
Uses for Coax Cut to Electrical Length
- Phasing lines: matching phase between stacked antennas or phased arrays
- Impedance matching: λ/4 section transforms impedance (see QWT calculator)
- Traps / stubs: open or shorted stubs for filtering (see Stub Tuner)
- Delay lines: timing reference in directional couplers
Always account for connector and fitting lengths when cutting phasing cables for stacked arrays or phased verticals. At VHF/UHF, a few centimeters of error is significant.
Stub Tuner Calculator
Formula
Stub length = (300 / f / 4) × VF meters (for λ/4 stub)
= (300 / f / 4) × VF × 3 (for 3λ/4 stub)
Stub Types
- Short-circuit λ/4 open stub: presents very high impedance (open circuit) at the design frequency. Used to notch (reject) an interfering signal.
- Short-circuit λ/4 shorted stub: presents very low impedance (short) at the design frequency. Used in bandpass filters and matching networks.
- Open-circuit stubs: opposite behavior — the λ/4 open stub acts as a short, and vice versa.
Tips & Tricks
- Stubs are inherently narrow-band. They work well for rejecting a single interfering carrier but do not help with broadband noise.
- A shorted λ/4 stub connected in parallel at a feed point adds a reactive component that can be used to tune out antenna reactance.
- TVI (TV interference) and BCI (broadcast interference) suppression often uses stub notch filters on the transmit feed line.
Modulation Index Calculator (AM / FM)
AM Formula
Modulation index m = Am / Ac
Sideband power = m²/2 × Pc
Total power @ 100% mod = 1.5 × Pc
FM Formula
Modulation index β = Δf / fm
Carson's rule BW = 2 × (Δf + fm)
Notes
- AM: m > 1.0 means overmodulation, which causes splatter (sideband energy beyond the intended bandwidth) and is illegal.
- FM: β < 0.3 is narrowband FM (NBFM, used in land mobile radio). β > 1 is wideband FM (broadcast, wide-deviation amateur FM).
- Amateur FM voice typically uses ±5 kHz deviation (NBFM) on VHF/UHF repeaters.
- Carson's rule contains ~98% of the total FM signal power; the actual bandwidth is theoretically infinite (Bessel function sidebands).
Bandwidth Estimator
Key Bandwidths by Mode
- AM DSB: BW = 2 × highest audio freq. A 3 kHz audio bandwidth needs 6 kHz RF bandwidth.
- SSB: BW = highest audio freq. Half the bandwidth of DSB-AM.
- FM: BW = 2(Δf + fm) by Carson's Rule.
- CW: Theoretical BW ≈ WPM × 0.8 Hz. Practical receivers use 250–500 Hz filters.
- PSK31: ~31 Hz. Remarkably narrow — hundreds of QSOs can fit in the voice portion of a band.
- FT8: ~50 Hz per signal; the protocol uses a 2.5 kHz window with many simultaneous signals.
- RTTY: 300–500 Hz for 170 Hz shift; wider for 850 Hz shift.
Tip: Narrow-bandwidth digital modes (PSK31, FT8, WSPR) can work with extremely weak signals that would be inaudible on SSB. FT8 routinely makes contacts at −20 dB SNR.
Data Rate vs. Bandwidth Calculator
Shannon Capacity (Theoretical Maximum)
C = B × log2(1 + SNR) bits/second
where B = bandwidth in Hz, SNR = linear signal-to-noise ratio
Nyquist Rate (No Noise)
R = 2B × log2(M) = 2B × n
where M = number of signal levels, n = bits per symbol
Notes
- Shannon capacity is a hard theoretical ceiling. Real systems approach but never reach it.
- Nyquist rate assumes a perfect (noiseless) channel. In practice, noise limits you to much less than the Nyquist rate.
- A 3 kHz SSB channel with 20 dB SNR has a Shannon capacity of ~20 kbps. Practical HF modems achieve 1–9.6 kbps.
- Increasing SNR (better antenna, lower noise) always increases capacity. Doubling bandwidth also doubles capacity (at high SNR), but only adds a few dB-worth of SNR gain.
SNR Calculator
Formulas
SNR (dB) = 10 × log10(Ps / Pn)
Noise floor = kTB + NF
kTB (dBm) = −174 + 10×log10(BW_Hz)
[at T = 290K, k = 1.38×10^−23 J/K]
Notes
- −174 dBm/Hz is the thermal noise power density at room temperature (290 K). This is the fundamental noise floor of any receiver.
- Noise figure (NF) is the amount by which a real receiver degrades the theoretical SNR. A good HF receiver has NF of 10–15 dB; a low-noise LNA might be 0.5–1 dB NF.
- Every 3 dB improvement in NF doubles the effective sensitivity.
- External noise (atmospheric, man-made) dominates at HF below ~20 MHz. On those bands, improving receiver NF below ~15 dB provides little real-world benefit.
Receiver Sensitivity Estimator (MDS)
Formula
MDS = kTB + NF + Required_SNR
kTB (dBm) = 10 × log10(kTB_watts) + 30
= 10 × log10(1.38×10^−23 × T × BW) + 30
MDS (Minimum Discernible Signal) is the weakest signal that can be detected at a given SNR threshold.
Typical Required SNR by Mode
- FT8: −20 dB (signal can be below the noise floor!)
- CW: ~3–10 dB for copy
- SSB voice: ~10–15 dB for readable copy
- FM (NBFM): ~12 dB for quieting; ~17 dB for full quieting
- AM: ~10 dB for acceptable intelligibility
Example: A receiver with 10 dB NF, 3 kHz bandwidth, and a 10 dB required SNR has MDS = −174 + 34.8 + 10 + 10 = −119 dBm.
RF Power Converter
Formulas
dBm = 10 × log10(P_mW) [ref: 1 mW]
dBW = 10 × log10(P_W) [ref: 1 W]
dBk = 10 × log10(P_kW) [ref: 1 kW]
dBk = dBW − 30
Key Reference Points
- 1 mW = 0 dBm
- 1 W = +30 dBm = 0 dBW
- 100 W = +50 dBm = +20 dBW = −10 dBk
- 1 kW = +60 dBm = +30 dBW = 0 dBk
- 1500 W = +61.8 dBm (US legal amateur HF limit)
Tips & Tricks
- Broadcast engineers use dBk; microwave engineers use dBm; amateur radio commonly uses W and dBm.
- Adding dB values multiplies powers: 100W + 3 dB = 200W; 100W − 3 dB = 50W.
- dBm is the standard unit in lab measurements with spectrum analyzers, signal generators, and power meters.
Transmitter Efficiency Calculator
Formula
Efficiency (%) = (Prf / Pdc) × 100
Heat dissipated = Pdc − Prf
Amplifier Class Reference
- Class A: 25–40% efficiency. Linear, low distortion. Transistor is always conducting. Used in low-level and SDR driver stages.
- Class B: ~60–78% efficiency. Two transistors share alternate half-cycles (push-pull). Used in linear amplifiers.
- Class AB: ~50–70% efficiency. Common in SSB linear PAs — compromise between linearity and efficiency.
- Class C: ~70–85% efficiency. Non-linear, used only for FM/CW where constant amplitude is acceptable.
- Class D/E/F: 85–95%+ efficiency. Switching amplifiers used in modern SDR-based PAs.
Tips & Tricks
- Heat sink sizing: size for the dissipated power, not the output power. A 100W Class A amp may dissipate 150–300W as heat.
- For a CW or FM rig, efficiency matters during key-down / continuous carrier. For SSB, average power is much lower than PEP, so duty cycle reduces average dissipation.
- Measure Pdc with a DC ammeter and voltmeter at the PA supply. Measure Prf into a calibrated dummy load.