The Shannon-Hartley Theorem calculator computes the theoretical upper limit data rate of a channel based on the bandwidth, receiver strength and channel noise.
INSTRUCTIONS: Choose units and enter the following:
- (B) Bandwidth of Channel
- (S) Received Power over Channel
- (N) Average Noise over Channel
Channel Capacity(C): The calculator returns the upper limit in bits per second. However, this can be automatically converted to compatible units via the pull-down menu.
The Math / Science
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. The Shannon-Hartley formula is:
C = B⋅log2(1 + S/N)
where:
- C = channel upper limit in bits per second
- B = bandwidth of channel in hertz
- S = received power over channel in watts
- N = mean noise strength on channel in watts
In communication channels affected by noise, the common bandwidth can vary significantly depending on the type of channel and the specific application. However, there are some general ranges for different types of communication channels:
- Telephone Lines (PSTN):
- Typical bandwidth: 300 Hz to 3.4 kHz
- Used for traditional voice communication with limited bandwidth.
- AM Radio:
- Typical bandwidth: 10 kHz per station
- AM radio channels have a bandwidth of about 10 kHz to accommodate the audio signal and avoid interference.
- FM Radio:
- Typical bandwidth: 200 kHz per station
- FM radio channels have a wider bandwidth to provide higher fidelity audio signals.
- Television Broadcast (Analog):
- Typical bandwidth: 6 MHz (NTSC) or 7-8 MHz (PAL/SECAM)
- Analog TV channels require several MHz of bandwidth for both audio and video signals.
- Wi-Fi (802.11 standards):
- Typical bandwidth: 20 MHz to 160 MHz (depending on the standard and channel bonding)
- Wi-Fi channels have variable bandwidths to support different data rates and to mitigate interference.
- Cellular Networks (e.g., LTE, 5G):
- Typical bandwidth: 1.4 MHz to 20 MHz (LTE), 10 MHz to 100 MHz (5G)
- Cellular channels have bandwidths that can be adjusted based on the available spectrum and requirements.
- Satellite Communication:
- Typical bandwidth: 1 MHz to 500 MHz (depending on the application and frequency band)
- Satellite channels can have a wide range of bandwidths to support various services, from voice and data to video broadcasting.
- Cable Modem (DOCSIS):
- Typical bandwidth: 6 MHz (downstream) and 3.2 MHz (upstream) per channel (DOCSIS 3.0)
- Cable modems use multiple channels to provide high-speed internet access.
The presence of noise in these channels can affect the quality of communication, and different modulation and error-correction techniques are employed to mitigate the impact of noise on the signal. The Shannon-Hartley theorem provides a theoretical upper limit to the channel capacity given the bandwidth and signal-to-noise ratio (SNR).
Telecommunications Calculators
- Propagation Delay Computes the delay between two routers based on their positions and a transfer rate.
- Nodal Delay: Computes the nodal delay based on the queuing, processing, transmission and propagation delay.
- End to End Delay Computes the end to end delay based on the number of nodes and the processing, transmission, and propagation delay.
- RF Velocity of Propagation: Computes the RF velocity based on the medium permittivity
- Transmission Delay: Computes the delay based on length of packet and transmission rate.
- Data Transfer Time Calculator Computes the time to transfer an amount of data based on the data transfer rate.
- Simplified Propagation Delay: Computes the delay between two router based on the distance and the transfer rate.
- Surge Impedance Loading: Computes the power loading of a transmission line.
- Amdahl's Law: Computes the total system speedup time based on the improvement of one portion.
- Signal-to-Noise Ratio (SNR) calculator: Computes a relative measure of the strength of the received signal (i.e., the information being transmitted) compared to the noise.
- Compute Data Storage Needed: Computes the approximate amount of data storage needed based on a period of time and a data rate.
- Network Propagation Delay Computes the propagation delay based on the positions of two routers and the propagation speed.
- Shannon-Hartley Theorem: Computes the theoretical upper limit data rate of a channel based on the bandwidth, receiver strength and channel noise.
- Cable dB Loss Budget Computes db loss based on length of fiber run and number of connectors.
- Voltage Resolution (Analog to Digital) Computes the Voltage Resolution of a measured analog signal over the nominal range [VL , VH] with a specified number of conversion bits.
- Effective Isotropically Radiated Power (EIRP): Converts an EIRP measured in mw (milliwatt) to the unitless ratio of dBm (ratio of decibel to 1 milli-unit).
- Length of Cable with Sag: Computes the length of cable between pole accounting for the sag.
References
- https://en.wikipedia.org/wiki/Logarithm