DESIGN OF A CUSTOM ASIC INCORPORATING CAN™ AND 1 ...

348sm
Cm 47 8 smbit
11-bit header
4
100
548sm
Cm 67 8 smbit
29-bit header
4
The term sm denotes the bounded size of message m in bytes. The term bit is the bit time of the
bus (on a bus running at 1 Mbps this is 1µs). The 34 (11-bit) term in the numerator comes from
the sum of the SOF, Arbitration, ACK, CRC, and Interframe Space bit fields whose values are 1,
12, 2, 16, and 3 respectively. For a 29-bit header, this value is 54 (sum of 1, 32, 2, 16, and 3).
The value of 47 (11-bit) in Equation 4.2 comes from the previous sum of 34 and the Control and
EOF bit fields whose values are 6 and 7 respectively. For a 29-bit header, the value is 67 (the
sum of 54 and the Control and EOF bit fields).
Equation 4.3 represents the queuing delay and is given by:
(4.2)
wm J j
bit
wm Bm Cj
(4.3)
j hpm Tj
The set hp(m) is the set of messages in the system of higher priority than m. Tj is the period of a
given message j, and Jj is the queuing jitter of the message. Bm is the longest time that the given
message m can be delayed by lower priority messages (this is equal to the time taken to transmit
the largest lower priority message), and can be defined by:
max B C
(4.4)
m k
k lp m
where lp(m) is the set of lower priority messages.
In Equation 4.3, the term wm appears on both sides of the equation, thus the equation
cannot be rewritten in terms of wm. A simple solution is possible by forming a recurrence
relationship: