Radiometrix
Battery Life ˜ 10 years = 87 000 hours
Using ˜ ½ of the battery capacity for t he PIC
15µA continuous drain = 15 ×10-6 × 87000 = 1.3Ah
AA lithium ˜ 2.3Ah leaves 1 Ah for transmissions
TX1 'ON' current - 10mA i.e.100hrs TX time in 10 years
= 100
10 × 365
= 0.274 hours per 24 hours
= 100 seconds 'ON' in 24hours
(864:1 duty cycle)
The Code
Assuming 3 transmissions every 24 hours
˜ 33 seconds TX Burst
First 3 seconds is preamble to allow lithium battery to stable.
Assuming 128 Bytes of data per transmission. (more than enough for energy
profiting.)
= ˜ 30 ms per bit
OFF time must be randomized.
suggest 8hours ± 4hours to avoid synchronization with other units.
Tones
Suggest logic '1' tone = 1024Hz (8 PIC µC cycles)
logic '0' tone = 819.2Hz (10 PIC µC cycles)
choose an exact bit time of 240 PIC microcontroller cycles = 29.297 ms
This is exactly 30 cycles for a logic '1' and 24 cycles for a logic 0.
Using 1 bit time = 2t i.e. reaches 83% of value by and of one bit
t = 29.297 = 14.65ms = 15 cycle of 1 or 12 cycle of 0
2
Hence, Q = tp = 15 × p
= 47 for logic 1 (1024 ) BPF
12 ×p = 37.7 for logic 0 (819.2 ) BPF
i.e. 3dB Band Width for each filter is 1024 = 819.2 = 21.8Hz
47 37.7
Hence, decoder 'noise' BW = 2 × 21.8 = 44Hz
Hence, noise reduction over RX1 AF output (5kHz) BW = 5000 = 20.5dB
'CLASH' AVOIDANCE PROBABILITY CALCULATIONS
For 1 TX Duty cycle = 33sec ON in 8hrs
˜1000:1 or 0.1% air usage.
For 2 TX's 'Clash' probability' = 1 in 333 or 0.3%
For N TX's Probability of loss of a burst
˜ (N-1) × 3 × (Tx on time)
= (N-1) × 0.3%
Tx off time
Probability of not getting an update after n tries
= (N-1)n
where N = number of units RX can hear
333
n = Number of tries
e.g:
