Friis transmission equation

Path loss = 20 log (4 * pi * r / lambda)

[Note: use log base 10]


Path loss = signal attenuation. Unit: dB

pi = 22 / 7

r = distance between transmitter and receiver. Unit: m

lambda = wavelength of signal. Unit: m

Wavelength = C/f


C = speed of electromagnetic waves in free space

= 299792458. Unit: m / s

f = frequency of signal. Unit: Hz

Let r = R * (2 ^ x)

Path loss = 20 log (4 * pi * R * L / lambda)

= 20 log (4 * pi * R / lambda) + 20 log (2 ^ x)

= 20 log (4 * pi * R / lambda) + 6x

The above derivation implies range(R) doubles every 6dB of path loss.

The path loss is +8.519dB more over a given range for the 2.4 GHz compared to 900MHz for the same range. In other words operating at 900 MHz exhibits a significantly longer range than is possible at 2.4 GHz.



Spectrum Diagrams

WiMAX articles

USB – Universal Serial Bus

USB is a polled cable bus with single-host-scheduled, token-based protocol.

Tiered-star topology: USB host is the root hub. A hub is center of a star. A star consists of point-to-point connections between [host and hub/function] or [hub and (another) hub/function].

Allowed topology: Maximum tiers = 7; Maximum non-root hubs in a tier = 5.

Data rates:

High-speed: 480 Mbps

Full-speed: 12 Mbps

Low-speed: 1.5Mbps

For effective utilization of bandwidth, full-speed and low-speed data can be transmitted at high-speed between host and hub, but transmitted between hub and device at full-speed or low-speed.

Operation: Clock is transmitted, encoded (NRZI encoding with bit stuffing) with differential data. A SYNC field precedes each packet for synchronization. The cable also carries VBUS (+5V at source) and GND to deliver power to devices. Cable with biased terminations at each end and up to seven metre length is allowed.

Most bus transactions involve the transmission of up to three packets. Each transaction begins when the Host Controller, on a scheduled basis, sends a USB packet describing the type and direction of transaction, the USB device address, and endpoint number. This packet is referred to as the “token packet.” The USB device that is addressed selects itself by decoding the appropriate address fields. In a given transaction, data is transferred either from the host to a device or from a device to the host. The direction of data transfer is specified in the token packet. The source of the transaction then sends a data packet or indicates it has no data to transfer. The destination, in general, responds with a handshake packet indicating whether the transfer was successful.

Some bus transactions between host controllers and hubs involve the transmission of four packets. These types of transactions are used to manage the data transfers between the host and full-/low- speed devices. The USB data transfer model between a source or destination on the host and an endpoint on a device is referred to as a pipe. There are two types of pipes: stream and message. Stream data has no USB-defined structure, while message data does. Additionally, pipes have associations of data bandwidth, transfer service type, and endpoint characteristics like directionality and buffer sizes. Most pipes come into existence when a USB device is configured. One message pipe, the Default Control Pipe, always exists once a device is powered, in order to provide access to the device’s configuration, status, and control information.

The transaction schedule allows flow control for some stream pipes. At the hardware level, this prevents buffers from under-run or overrun situations by using a NAK handshake to throttle the data rate. When NAKed, a transaction is retried when bus time is available. The flow control mechanism permits the construction of flexible schedules that accommodate concurrent servicing of a heterogeneous mix of stream pipes. Thus, multiple stream pipes can be serviced at different intervals and with packets of different sizes.