# 'How to Cheat': The Physics of RFID--Part III

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Editor's Note: Miss Part I? Part I Part II

**Performing Antenna Power Calculations**

To understand an antenna's performance, it's important to know how an antenna radiates power. For example, an isotropic (omnidirectional) antenna radiates power uniformly in all directions, whereas a directional antenna radiates power in a specific direction. The performance of an antenna related to the power it radiates can be understood in terms of three physical quantities: effective radiated power, power density, and link margin.

**Effective Radiated Power**

The effective radiated power (ERP) of an antenna in a specific direction is the power that will need to be supplied to a reference antenna to produce the same power this antenna is producing in this direction. Therefore, by definition of antenna gain, the ERP can be written as:

_{t}x A

_{g}

Where A_{g} is the antenna gain and P_{t} is the total power transmitted by the antenna, which can be expressed in the following equation:

_{}= RF power - cable loss

After power is transmitted by an antenna, it spreads out into the space. Therefore, the power density (power per unit space) is an important quantity.

*Power Density*

An EM wave transmitted from an antenna travels in all directions in the form of an expanding spherical wavefront. The power density can be looked upon as the power of this wave per unit of surface area of the sphere. The surface area of a sphere with radius R is
4πR^{2}. Therefore, the power density, P_{d} at a distance R from the transmitter antenna can be calculated using the following formula:

_{d}= P

_{t}/(4πR

^{2})

P_{t}is the total power radiated by the antenna. This formula works for the power being
emitted by an isotropic antenna. If the antenna is a directional antenna, we need to take into
account the antenna gain, and the formula used to calculate the power density is as follows:

_{d}= EPR / (4πR

^{2}) = (P

_{t}X A

_{g})/(4πR

^{2})

Once the antenna has radiated energy, bad things, in addition to the natural spreading out, can happen to it while it's on its way to the destination. For example, it may be absorbed or reflected back by some materials on its way. ERP does not account for what happens to the energy wave on its way to the destination and how it is received by the receiving antenna. However, the overall system performance depends on how much power is being transferred between the transmitter and the receiver. The quantity that includes the travel and the receiving part of communication is called link margin.

**Link Margin**

Link margin quantifies the performance of the overall RFID communication system, including the transmitting antenna and the receiving antenna. The link margin, L_{m}, can be defined as:

_{m}= (ERP

_{r}/P

_{min}) = (ERP

_{t}- A

_{rg})/P

_{min}= (P

_{t}- A

_{tg}- A

_{rg})/P

_{min}

_{t}- A

_{tg}- A

_{rg})/P

_{min}) 10 - (log P

_{t}+ log A

_{tg}+ log A

_{rg}- log P

_{min})

where:

P_{t} = Transmitted power

A_{tg} = Gain for transmitter antenna

A_{rg} = Gain for receiving antenna

P_{min} = Minimum received signal strength

Looking at this equation, you can realize that link margin is the ratio of the maximum effective signal strength received to the minimum signal strength received. In RFID, it means the amount of power that a tag can extract from the RF signal before the communication between the tag and the reader weakens.

So, the link margin takes into account the impacts of both the transmitting antenna and the receiving antenna. It also includes the factor of minimum received signal strength. The received signal strength varies and is less than the transmitted signal strength due the interaction of the signal with the medium through which it travels.

Next: The Travel Adventures of RF Waves

**About the Authors**

Frank Thornton, Owner, Blackthorn Systems, New Hampshire, USA; and Paul Sanghera, Educator, technologist, and an entrepreneur, California, USA

Printed with permission from Syngress, a division of Elsevier. Copyright2008. "How to Cheat at Deploying and Securing RFID" by Frank Thornton and Paul Sanghera. For more information about this title and other similar books, please visit ElsevierDirect.