Communications Formulas
Communications formulas relate bandwidth, data rate, and signal-to-noise ratio to channel capacity and link reliability. These calculators help you budget gains and losses across a transmission path. They are essential for wired and wireless link planning.
Communications Formula Calculators
- UART Baud Rate Error Error% = |actual − target| / target × 100 Actual Baud Rate 5 Hz, Target Baud Rate 11 Hz → Baud Error = 0.5455 %
- RS-485 Termination Resistor R = Z_cable Cable Impedance 2.2 Ω → Termination Resistance = 2.2 Ω
- RS-485 Bias Resistor R_bias = (Vcc − V_diff_min) / I_bias Supply Voltage 3.3 V, Min Differential Voltage 1.55 V, Bias Current 1 mA → Bias Resistance = 1.75 kΩ
- Shannon Channel Capacity C = B × log₂(1 + SNR) Bandwidth 11 Hz, SNR (linear) 0.025 → Channel Capacity = 0.3919 Hz
- Bit Error Rate (BPSK) BER = 0.5 × erfc(√(Eb/N0)) Eb/N0 0.3 dB → Bit Error Rate = 0.07161
- Wireless Link Range d = f(Ptx, Gtx, Grx, sensitivity, freq) TX Power -2 dB, TX Antenna Gain 0.2 dB, RX Antenna Gain 0.44 dB, Receiver Sensitivity -4.4 dB, Frequency 100 kHz → Range = 0.3388 km
- Manchester Encoding Bandwidth BW = 2 × bitrate Bit Rate 11 Hz → Bandwidth = 22 Hz
- I²C Pull-up Resistor R_max = t_rise / (0.8473 × C_bus) Rise Time 100 ps, Bus Capacitance 1 pF → Pull-up Resistance = 118 Ω
Worked result for every Communications formula
| Formula | Expression | Worked result |
|---|---|---|
| UART Baud Rate Error | Error% = |actual − target| / target × 100 | Actual Baud Rate 5 Hz, Target Baud Rate 11 Hz → Baud Error = 0.5455 % |
| RS-485 Termination Resistor | R = Z_cable | Cable Impedance 2.2 Ω → Termination Resistance = 2.2 Ω |
| RS-485 Bias Resistor | R_bias = (Vcc − V_diff_min) / I_bias | Supply Voltage 3.3 V, Min Differential Voltage 1.55 V, Bias Current 1 mA → Bias Resistance = 1.75 kΩ |
| Shannon Channel Capacity | C = B × log₂(1 + SNR) | Bandwidth 11 Hz, SNR (linear) 0.025 → Channel Capacity = 0.3919 Hz |
| Bit Error Rate (BPSK) | BER = 0.5 × erfc(√(Eb/N0)) | Eb/N0 0.3 dB → Bit Error Rate = 0.07161 |
| Wireless Link Range | d = f(Ptx, Gtx, Grx, sensitivity, freq) | TX Power -2 dB, TX Antenna Gain 0.2 dB, RX Antenna Gain 0.44 dB, Receiver Sensitivity -4.4 dB, Frequency 100 kHz → Range = 0.3388 km |
| Manchester Encoding Bandwidth | BW = 2 × bitrate | Bit Rate 11 Hz → Bandwidth = 22 Hz |
| I²C Pull-up Resistor | R_max = t_rise / (0.8473 × C_bus) | Rise Time 100 ps, Bus Capacitance 1 pF → Pull-up Resistance = 118 Ω |
Variables used across Communications formulas
- Error% — Percentage deviation from target baud rate
- Actual — The baud rate actually achieved by the hardware (baud)
- Target — The desired baud rate (baud)
- R — Termination resistance in ohms (Ω)
- Z — Characteristic impedance of the cable in ohms (Ω)
- Vcc — Supply voltage (V)
- V_diff_min — Minimum required differential voltage (V)
- I_bias — Required bias current (A)
- C — Channel capacity in bits per second (bps)
- B — Channel bandwidth in hertz (Hz)
- SNR — Signal-to-noise ratio (linear, not dB)
- BER — Bit error rate (dimensionless probability)
- Eb/N0 — Energy per bit to noise spectral density ratio (dB)
- d — Maximum range (m)
- Ptx — Transmit power (dBm)
- Gtx — Transmit antenna gain (dBi)
- Grx — Receive antenna gain (dBi)
- sensitivity — Receiver sensitivity threshold (dBm)
- f — Operating frequency (Hz)
- BW — Required bandwidth in hertz (Hz)
- bitrate — Data rate in bits per second (bps)
- t_rise — Maximum allowed rise time (s)
- C_bus — Total bus capacitance (F)
Questions people ask about Communications
- Bit error rate bpsk awgn eb/n0 formula — Bit Error Rate (BPSK)
Related Formula Categories
Browse the full formulas index for all 32 categories.