Motorola CDR500 Programming Manual page 59

CDR500 & CDR700 Repeater Service Manual
manufacturers rate battery capacity based on the cur-
rent drawn over a five (5), ten (10) or twenty (20) hour
period. In terms of capacity, these are referred to as
0.2C, 0.1C and 0.05C rates, respectively. They are not
linearly related; doubling the current drain will most
likely reduce the time available by more than half.
Ambient temperature has a profound effect on the bat-
tery capacity. At -20˚C (only 4 degrees below zero Fahr-
enheit!), approximately half of the capacity of room
temperature is available.
Example:
What "size" battery do you need? Let's assume that
you customer's repeater is in a location that experi-
ences power outages that require battery backup for no
more than 5 hours. The repeater operates at a 66%
transmit duty cycle. The transmitter is on the air an
average of 2 minutes and the repeater is then in
standby/receive for 1 minute. The total cycle time is 3
minutes. The repeater transceiver draws 14A of current
during transmit and 1.5A during receive. The repeater
is using an external controller. The controller and the
fan of the repeater add 0.5A to the current drains of
transmit and receive. Therefore, for 2 minutes the bat-
tery must supply 14.5A and for the next 1 minute the
battery must supply 2A. Then, the cycle repeats for a
total of 5 hours.
Let the battery operating "capacity" be represented by
C . This is based on the current drains during trans-
op
mit and receive, the percentage of times of each and the
total time required for battery operation. C
represented by the following equation:

× ×
Cop = Ttotal Itx

where:
Cop = Operating capacity in Ampere-hours (A-h)
Ttotal = Total time the station is on battery power
(in hours) = 5 hours
Itx = Total current drain during transmit
(in Amperes) = 14.5A
Irx = Total current drain during receive/standby
(in Amperes) = 2A
Ttx = Transmit time during a single cycle
(in minutes) = 2 minutes
Trx = Receive time during a single cycle
(in minutes) = 1 minute
Tcycle = Cycle time (in minutes) = 3 minutes
March, 2001
may be
op
 
Ttx Trx
×
----------------- - + Irx ----------------- -
 
Tcycle Tcycle
Therefore:
×
Cop = 5
Cop = 65
Now, how big is it? Let's consider the rated battery
capacity, C, as a function of the C
An approximation to the rated battery capacity can be
calculated with the following equation:
C Cop
where:
C = Rated battery capacity in Ampere hours (A-h)
Tcr = Rated battery discharge time in hours (usually 5,
10, or 20 hours)
Top = Time, in hours, that the repeater will be operating
on the battery
0.1 = Raise the term Tcr / Top to the 0.1 power
A scientific calculator or the functions in a speadsheet
program can be used to solve the equation.

For our example, let's consider the 65 A-h operating

capacity, over 5 hours of operating on battery, and
rated battery discharge times of 5 hours, 10 hours, and
20 hours.
1. Tcr = 5 hours
A 65 A-h (0.2C) battery would provide the required
energy at room temperature environment.
2. Tcr = 10 hours
C 69.7
6864110R66-O
Battery Capacity
  
2
× ×
14.5 -- - + 2
  
3
calculated above.
op
0.1
 
Tcr
≈ ×
--------- -
 
Top
0.1
 
5
≈ ×
-- -
C 65
 
5
≈
C 65
0.1
 
10
≈ ×
C 65 ----- -
 
5
≈
Battery Revert

1
-- -

3
7-3