dBHz
How Decibel-Hertz Is Defined and Used
The decibel-hertz unit takes a quantity measured in hertz and places it on a logarithmic scale using 10 times the base-10 logarithm. The most important everyday use is the carrier-to-noise-density ratio C/N0, the ratio of received carrier power to the noise power spectral density N0 measured in one hertz of bandwidth. Because the denominator is referenced to a 1 Hz slice, the ratio has units of hertz and is reported in dB-Hz. This makes C/N0 a property of the link itself: transmit power, antenna gains, path loss, and system noise temperature set its value, but the receiver bandwidth does not.
That bandwidth independence is what makes dB-Hz so useful in receiver design. A GNSS engineer can quote a single C/N0 number and then derive the predetection signal-to-noise ratio for any chosen predetection or correlator bandwidth by subtracting that bandwidth in dBHz. The same number feeds directly into the energy-per-bit to noise-density ratio Eb/N0 simply by subtracting the data rate expressed in dBHz, tying the analog link budget to the digital error-rate budget without changing reference frames.
The conversion arithmetic is simple but worth keeping straight. Every factor of ten in frequency adds 10 dBHz, and every factor of two adds about 3 dBHz, so a 2 MHz noise bandwidth is roughly 63 dBHz and a 5 MHz channel is about 67 dBHz. Care is needed not to confuse the noise-equivalent bandwidth, the integral of the normalized filter response, with the 3 dB bandwidth; for a real filter the noise bandwidth is typically 5 to 15 percent wider, which shifts the dBHz value by a few tenths of a dB.
Link-Budget Equations Involving dBHz
BdBHz = 10 × log10(B / 1 Hz)
e.g. 1 MHz → 10 × log10(106) = 60 dBHz
Carrier-to-noise-density (C/N0):
C/N0 (dB-Hz) = SNR (dB) + 10 × log10(B)
equivalently C/N0 = PC (dBW) − N0 (dBW/Hz), with N0 = kTsys
k = 1.38 × 10−23 J/K (so kTsys = −204 dBW/Hz at 290 K)
Energy-per-bit ratio:
Eb/N0 (dB) = C/N0 (dB-Hz) − 10 × log10(Rb)
Where B = noise bandwidth (Hz), Rb = bit rate (bit/s), k = Boltzmann constant, T = system noise temperature (K). Example: C/N0 = 45 dB-Hz, B = 2 MHz (63 dBHz) → SNR ≈ −18 dB.
dBHz Reference Values and Related Decibel Units
| Unit / Quantity | Reference | Formula | Typical Value | Where Used |
|---|---|---|---|---|
| dBHz (1 kHz) | 1 Hz | 10 log10(103) | 30 dBHz | Narrowband loop bandwidth |
| dBHz (1 MHz) | 1 Hz | 10 log10(106) | 60 dBHz | Channel / noise bandwidth |
| C/N0 (GPS L1) | N0 in 1 Hz | C − N0 | 40 to 50 dB-Hz | GNSS acquisition / tracking |
| C/N0 (Ku/Ka downlink) | N0 in 1 Hz | EIRP + G/T − L | 70 to 90 dB-Hz | VSAT, broadcast satellite |
| dB | dimensionless | 10 log10(P1/P2) | 0 to 60 dB | Gain, loss, ratios |
| dBm | 1 mW | 10 log10(P/1 mW) | −120 to +30 dBm | Absolute power levels |
Frequently Asked Questions
How does dBHz differ from dB and dBm?
Plain dB is dimensionless, a ratio of like quantities used for gain or loss. dBm references absolute power to 1 mW. dBHz references a frequency or bandwidth in hertz: X dBHz equals 10 × log10 of the value in hertz, so 1 MHz (106 Hz) is exactly 60 dBHz. Because dBHz carries a hertz unit inside the logarithm, it is not interchangeable with the dimensionless dB used for amplifier gain or cable loss.
How is carrier-to-noise-density ratio C/N0 in dB-Hz related to SNR?
C/N0 (dB-Hz) = SNR (dB) + 10 × log10(B), where B is the receiver noise bandwidth. Because C/N0 normalizes out bandwidth, it describes the link itself and stays fixed when you change the filter. For a GNSS receiver at C/N0 = 45 dB-Hz with a 2 MHz predetection (front-end) bandwidth (63 dBHz), predetection SNR is about −18 dB, recovered through correlation processing gain. The carrier and code tracking loops run much narrower, only a few hertz to tens of hertz wide.
What is a typical C/N0 value for a satellite or GNSS link?
Healthy GPS L1 C/A signals run 40 to 50 dB-Hz; below 35 dB-Hz indicates blockage, multipath, or interference, and acquisition usually fails below about 30 dB-Hz. Ku-band and Ka-band downlinks are engineered for 70 to 90 dB-Hz so that, after subtracting the channel bandwidth, several dB of Eb/N0 margin remains. Deep-space links may sit near 10 to 20 dB-Hz with very low symbol rates and heavy coding.