Application Note: 102
under FCC Regulation Part 15, Section 231, Paragraph (e)

Radiometrix modules operate on license exempt frequencies of 418MHz or 433.92MHz. Their Effective Radiated Power (ERP) outputs and spurious emissions meet the UK and European

Type approval requirements. However, Electric Field Strength limit imposed by FCC is very much lower than European power limit as shown below.
Figure 1: Electric Field Strength limits on signal & spurious emission
 
The following Table shows the conversion from dBm to Electric Field Strength in m V/m for common power and spurious emission level

Power

P (dBm)

E (mV/m) @3m

E (dBmV/m) @3m

 Comments

10mW

10

182,574

105.2
European limit for 433.92MHz

1mW

0

57,735

95.2
Typical 418MHz modules

0.25mW

-6

28,868

89.2
UK limit for 418MHz modules

5.8m W

-22

4399

72.9
FCC limit for 433.92MHz

5.1m W

-23

4133

72.3
FCC limit for 418MHz
75nW
-41
500
54
FCC Spurious Emission limit for >470MHz

1m W

-30

1,826

65.2
European Spurious Emission limit for
> 1 to 4GHz

0.25m W

-36

915

59.2
European Spurious Emission limit for
25-47, 74-87.5, 118-174, 230-470, 862-1000 MHz

4nW

-54

115

41.2
European Spurious Emission limit for
47-74, 87.5-118, 174-230, 470-862 MHz

The above limitations on Electric Field Strength would require
25dB (max) power attenuation on 418MHz modules
35dB (max) power attenuation on 433.92MHz module.

The above values are only required if used with a high gain antennas like dipole or yagi antenna.

When using antennas like 1/4 wavelength whip, helical or loop antenna, ERP will be less than the Power Output at the RF pin of the Transmitter. i.e. required attenuation value will be few dBs less than the calculated values.

Note: An imperial 'rule of thumb' for in-building operation requires a 15dB change in path loss capability to change the range by a factor of two. This is a very cruel law when compared to free space propagation where only a 6dB change is required to double / halve the range.

To reduce the Effective Radiated Power (ERP) either one of the following can be used:

1. Passive attenuation network
2. Very short monopole antenna

Figure 2: Methods to reduce ERP
The following Table gives Pi-Network Resistor values for Attenuators (50W )

Attenuation (dB)

R1 (W )

R2 (W )

5

179

30

10

96

71

15

72

136

20

61

248

25

56

443

30

53

790

35

52

1405
It is recommended that the above Pi-Network is implemented with a good ground plane using Surface Mount Resistors.
 
Power or Electric Field Strength Equation
Equation (1)
   
where Pr received power density [W/m2]
  Pt transmitted power [W]
  G numerical gain of the transmitting antenna relative to an isotropic source
  r distance of the measuring point from the electrical center of the antenna in meters
  E electric field strength [V/m]
  So characteristic impedance of free space [W ]
   
 
FCC specifies limit in terms of the Electric Field Strength in m V/m at a distance of 3m.
Using Equation (1),
When G=1, r=3m, So@ 120p W,
Equation (2)