Link Budget and System Architecture Link Budget Calculation Informational

What is the difference between C/N, Eb/No, and SNR and when do I use each one?

Q: What is the difference between Eb/No and SNR?

SNR (signal-to-noise ratio) = C/N measured in the receiver bandwidth. It is the same as C/N for a single carrier. Eb/No = SNR × (B/R_b). For a system where B = R_b: Eb/No = SNR numerically. For OFDM (5G NR): the "SNR" reported by the receiver is typically the per-subcarrier SNR (the signal power on one subcarrier divided by the noise on that subcarrier). This per-subcarrier SNR ≈ Es/No (because each subcarrier carries one symbol, and the noise bandwidth equals the subcarrier spacing). So: per-subcarrier SNR ≈ Es/No = Eb/No + 10×log10(bits per symbol). The relationship between SNR and Eb/No depends on the modulation and system bandwidth definition.

Q: How is C/N measured in practice?

For CW signals: use a spectrum analyzer. Measure the carrier power (C) as the peak power in the signal bandwidth. Measure the noise floor (N) in the same bandwidth. C/N = C - N (in dB). For modulated signals: use a modulation analyzer or wideband power meter. Measure the total signal power in the channel bandwidth. Measure the noise power in an adjacent empty channel (of the same bandwidth). C/N ≈ signal power - adjacent noise power (in dB). For digital signals: the receiver typically computes EVM, which is related to C/N by: C/N ≈ -20×log10(EVM). This is the most accurate method because it accounts for all impairments (noise, distortion, interference).

Q: How much Eb/No margin do I need?

The link margin is the difference between the available Eb/No and the required Eb/No: margin = Eb/No_available - Eb/No_required. Recommended margins: clear-sky (nominal conditions): 3-6 dB. This accounts for: implementation losses (real vs ideal receiver: 1-2 dB), component tolerances (0.5-1 dB), temperature variation (0.5-1 dB), and miscellaneous losses. Rain fade (satellite links): additional 3-15 dB depending on the frequency (20+ GHz) and the availability requirement (99.5% vs 99.99%). Multipath fading (terrestrial mobile): additional 10-40 dB (depending on the environment and the diversity techniques used). A link budget must include all margin allocations to ensure reliable operation under the worst-case conditions.

C/N (carrier-to-noise ratio) and Eb/No (energy per bit to noise spectral density) are two different ways to express the signal quality in a communication link, each suited for different analyses: (1) C/N (carrier-to-noise ratio): the ratio of the total carrier power (C) to the total noise power (N) within the receiver bandwidth. C/N = C / N = C / (k × T × B), where k = Boltzmann constant (1.38 × 10^-23 J/K), T = system noise temperature (K), and B = receiver bandwidth (Hz). C/N is a bandwidth-dependent metric: if the bandwidth changes, the noise (N = kTB) changes, and C/N changes even though the signal quality has not changed. C/N is directly measurable: connect a spectrum analyzer or power meter to the receiver and measure the signal power and noise floor. C/N is used for: analog systems (FM, AM) where the signal quality depends on the total signal-to-noise ratio, and as an intermediate step in link budget calculations. (2) Eb/No (energy per bit to noise spectral density): the ratio of the energy per information bit (Eb) to the noise power spectral density (No). Eb = C / R_b (energy per bit = carrier power / bit rate). No = k × T (noise spectral density). Eb/No = (C/R_b) / (k × T) = (C/N) × (B/R_b). Eb/No is bandwidth-independent: it depends only on the carrier power, bit rate, and noise temperature. Eb/No is the fundamental metric for digital modulation performance: the BER (bit error rate) for any modulation scheme is a function of Eb/No alone. For example: BPSK: BER = Q(sqrt(2 × Eb/No)). QPSK: BER = Q(sqrt(2 × Eb/No)) (same as BPSK per bit). 16-QAM: BER ≈ (3/8) × Q(sqrt(4 × Eb/(5 × No))). Each modulation scheme has a well-defined BER curve that specifies the required Eb/No for a target BER. (3) Conversion: Eb/No (dB) = C/N (dB) + 10 × log10(B/R_b). The term 10 × log10(B/R_b) is the "processing gain" or "bandwidth expansion factor." For a system where B = R_b (bandwidth exactly equals the bit rate, ideal Nyquist bandwidth): Eb/No = C/N. For a system with bandwidth expansion (spread spectrum, OFDM with guard interval): B > R_b, so Eb/No > C/N.

Category: Link Budget and System Architecture

Updated: April 2026

Product Tie-In: Antennas, Amplifiers, Cables

C/N vs Eb/No Explained

Understanding the distinction between C/N and Eb/No is fundamental to communication system design. They answer different questions: C/N asks "how strong is my signal relative to noise?" while Eb/No asks "is each bit received reliably?"

When to Use Each

(1) Use C/N when: performing a link budget (calculating the received signal power, path loss, antenna gain, and comparing to the noise level). Specifying the performance of a satellite transponder or relay (the transponder does not know the modulation or bit rate; it just amplifies the carrier). Measuring the signal quality on a spectrum analyzer. Comparing with interference (C/I: carrier-to-interference ratio). (2) Use Eb/No when: determining the BER for a specific modulation scheme. Comparing different modulation schemes (since BER vs Eb/No is bandwidth-independent, different modulations can be compared directly). Specifying the required link quality for a digital service (e.g., "the link must provide Eb/No > 10 dB for BER < 10^-6 with QPSK"). Link margin analysis (the margin = available Eb/No - required Eb/No for the target BER). (3) Link budget flow: calculate C/N from the link budget → convert to Eb/No using the bandwidth and bit rate → look up the required Eb/No for the modulation and coding scheme → determine the link margin.

Es/No and EVM

(1) Es/No (energy per symbol to noise density): for multi-bit modulations (QPSK, 16-QAM, 64-QAM): each symbol carries multiple bits. Es = Eb × log2(M), where M = modulation order (4 for QPSK, 16 for 16-QAM). Es/No = Eb/No + 10×log10(log2(M)). For 64-QAM: Es/No = Eb/No + 7.78 dB. Es/No is the more natural metric for constellation-based analysis (the symbol error rate depends on Es/No). (2) EVM (error vector magnitude): the RMS error between the ideal and received constellation points. EVM is related to SNR (and thus Eb/No) by: EVM_rms ≈ 1/sqrt(SNR) = 1/sqrt(Es/No). For 64-QAM with EVM < 8% (-22 dB): Es/No > 22 dB → Eb/No > 22 - 7.78 = 14.2 dB. (3) In 5G NR: the performance requirements are specified in terms of EVM: QPSK: EVM < 17.5% (-15.1 dB). 16-QAM: EVM < 12.5% (-18.1 dB). 64-QAM: EVM < 8% (-21.9 dB). 256-QAM: EVM < 3.5% (-29.1 dB). These can be converted to Eb/No requirements for link budget analysis.

C/N and Eb/No Equations

C/N = C/(kTB)
Eb/No = (C/R_b)/(kT) = C/N × (B/R_b)
BPSK BER = Q(√(2Eb/No))
Es/No = Eb/No + 10log₁₀(log₂M)
EVM_rms ≈ 1/√(Es/No)

Common Questions

Frequently Asked Questions

What is the difference between Eb/No and SNR?

SNR (signal-to-noise ratio) = C/N measured in the receiver bandwidth. It is the same as C/N for a single carrier. Eb/No = SNR × (B/R_b). For a system where B = R_b: Eb/No = SNR numerically. For OFDM (5G NR): the "SNR" reported by the receiver is typically the per-subcarrier SNR (the signal power on one subcarrier divided by the noise on that subcarrier). This per-subcarrier SNR ≈ Es/No (because each subcarrier carries one symbol, and the noise bandwidth equals the subcarrier spacing). So: per-subcarrier SNR ≈ Es/No = Eb/No + 10×log10(bits per symbol). The relationship between SNR and Eb/No depends on the modulation and system bandwidth definition.

How is C/N measured in practice?

For CW signals: use a spectrum analyzer. Measure the carrier power (C) as the peak power in the signal bandwidth. Measure the noise floor (N) in the same bandwidth. C/N = C - N (in dB). For modulated signals: use a modulation analyzer or wideband power meter. Measure the total signal power in the channel bandwidth. Measure the noise power in an adjacent empty channel (of the same bandwidth). C/N ≈ signal power - adjacent noise power (in dB). For digital signals: the receiver typically computes EVM, which is related to C/N by: C/N ≈ -20×log10(EVM). This is the most accurate method because it accounts for all impairments (noise, distortion, interference).

How much Eb/No margin do I need?

The link margin is the difference between the available Eb/No and the required Eb/No: margin = Eb/No_available - Eb/No_required. Recommended margins: clear-sky (nominal conditions): 3-6 dB. This accounts for: implementation losses (real vs ideal receiver: 1-2 dB), component tolerances (0.5-1 dB), temperature variation (0.5-1 dB), and miscellaneous losses. Rain fade (satellite links): additional 3-15 dB depending on the frequency (20+ GHz) and the availability requirement (99.5% vs 99.99%). Multipath fading (terrestrial mobile): additional 10-40 dB (depending on the environment and the diversity techniques used). A link budget must include all margin allocations to ensure reliable operation under the worst-case conditions.

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