Simulation of H1 Networks
1990
Published With Permission of Fisher Rosemount Inc. (Austin, TX).
1. Introduction
The H1 topologies permit all of the following:
1. Total cable lengths up to 1900 meter.
2. Drops of relatively long and varying lengths,
located anywhere along the trunk.
3. Up to 32 devices per network, each having
a relatively low device impedance of 3000 ohm.
4. Mixing of different cables in a given network.
Given this desired degree of latitude in constructing networks, there
do not appear to be any simple rules or first-order approximations
that can be applied to insure that attenuation and delay distortion
are within acceptable limits. It is not satisfactory to simply state
the desired attenuation and distortion limits. These are not
configuration rules. Rather they are the desired outcome of applying
the rules.
To make it easy to build conformant networks, the network
configuration rules should consist of limits on drop and trunk lengths.
These limits can be based on simulations. To this end, we present this
report. Although more work remains to be done, the information
provided illustrates what can be achieved.
2. Simulation Description
The simulation assumes that every network consists of the parts shown in figure 1. The trunk is a single homogeneous length of cable, as is each drop. The trunk has a terminator at each end consisting of a resistor and capacitor in series. Each drop has a load at the end opposite the trunk, consisting of a resistor and capacitor in parallel. Each cable segment of figure 1 is modeled as a doubly-loaded transmission line, with each load being the driving point impedance of a combination of other lumped and distributed elements.
Figure 1 -- Network Model
Although the figure illustrates a BUS network, the simulations can
be applied to the TREE network as well. The TREE is just a special
case of the BUS in which all drops are located at one end of the trunk.
The simulation is divided into two stages. In the first stage, a
large number of networks are constructed and each is analyzed. The
worst transmission path of the worst network is found. In the 2nd
stage, a large number of data streams are generated. Each is
Manchester encoded and sampled. The samples are transformed to the
frequency domain and the result is filtered using the worst case
transfer function found in the first stage of simulation. The
frequency domain information is transformed back to the time domain.
All waveforms are then either plotted or else searched for the worst
(smallest) eye opening among all waveforms.
2.1 First Stage Simulation
The first stage of simulation needs a criterion for the worst transmission path of the worst network. There are actually three different criteria that are used. These are
1. Maximum Magnitude Ratio between any two
frequencies in the 0.25 Fr to 1.25 Fr band.
2. Maximum Delay Difference between any two
frequencies in the 0.25 Fr to 1.25 Fr band.
3. Maximum Attenuation at any frequency
in the 0.25 Fr to 1.25 Fr band.
Consequently, when the first stage of the simulation is run, there are
3 different transfer functions found -- one for each of these worst-
case conditions. The 2nd stage of simulation can use any one of these
transfer functions.
The input to the first stage of simulation consists of all of the
following:
1. Number of networks to be "built."
2. Number of devices.
3. Range of frequencies over which transfer function is to
be retained.
4. Trunk length or total cable length.
5. Drop length or range of drop lengths.
6. Measured cable data.
7. The values of terminator elements at each end of the trunk.
8. The values of load elements at the non-trunk end of
each drop.
When the trunk length is specified, the total cable length consists of
this length and all of the drop lengths. When total cable length is
specified, the trunk is diminished by the amount of the drop lengths.
The trunk cable type can either be specified or else selected randomly
from a group of cables.
Each drop is separately specified. Its location on the trunk is
randomly selected within specified limits. For example, drop number 3
can be specified to be located anywhere along the trunk within a range
of 0.8 to 0.83 of the trunk, with 0 being one end of the trunk and 1
being the other end. By specifying 0 and 1 for the limits for all
drops, a BUS is constructed. By specifying 0.9999 and 1 as the limits
a TREE is constructed.
The drop length can be specified or else its length can be selected
randomly from 0 to a specified limit. The cable used for the drop can
also be specified or else randomly selected from the group of cables.
Both trunk terminators are assumed identical. All drop loads are
also assumed identical.
The transmitting device is applied to each drop (opposite the trunk
end) and to each end of the trunk. If there are N drops, then there are
N+2 locations at which the transmitting device is attached and
(N+1)(N+2)/2 unique signal paths. A network having two drops and 6
unique transmission paths is illustrated in figure 2. If the locations
for the transmit device are numbered 0 through 3, then the unique
paths are:
0 ---> 1
0 ---> 2
0 ---> 3
1 ---> 2
1 ---> 3
2 ---> 3
Figure 2
Unique Signal Paths For A Two-Drop Network
The transmitting device is assumed to be a current source. Consequently, the transfer functions are initially transimpedances. That is, they have a current input and voltage output. Each transimpedance is then normalized to the real part of the trunk terminator divided by two, so that it becomes a true transfer function. In other words, each transfer function is a comparison of an actual path to an ideal "path" consisting of just a pure resistance.
2.2 Second Stage Simulation
In the 2nd stage many random waveforms are generated. Each starts
as a random bit stream. The random bit stream is then Manchester
encoded. Following encoding, each Manchester waveform is trapezoidally
shaped. The waveform is 0.9 millisecond in duration so that it
contains approximately 28 bits.
The waveform slope is chosen to reduce the 3rd harmonic to zero.
The waveform is sampled and FFTed to the frequency domain. Various
filters are then applied. The first filter is a single-pole high-pass
filter at 0.25 Fr. The second filter is a low-pass filter at 1.25 Fr.
The purpose of these filters is to remove the small amount of signal
energy that exists at the extremes of the Manchester power spectrum. A
second purpose is to provide a gradual transition region between the
band edges and a truncation filter which is applied at 4 kHz and 80 kHz
(0.128 Fr and 2.56 Fr). The truncation filter truncates the spectrum
so that everything below 4 kHz and above 80 kHz is set to zero, thereby
reducing the amount of computation. Another reason that the spectrum
is truncated is that cable data is only available from 1 kHz to 100
kHz. The combined single-pole and truncation filtering is illustrated
in figure 3.
Figure 3
Single-Pole and Truncation Filters
3. How Many Networks?
As the number of networks used in a given simulation is increased,
the program is able to find networks and network paths that are
progressively worse. However, simulations using 100, 200, 500, and
1000 networks show that above 100 networks; the worst distortion is
only a few percent greater than that found at 100 networks.
Similarly, in the 2nd stage of the simulation, very little is
gained by using more than 100 waveforms in the eye diagram. Therefore,
throughout nearly all of the simulations, 100 networks were used and
100 waveforms were generated for each worst-case transfer function.
4. Analysis Conditions
To keep the amount of data manageable, it is necessary to narrow the
analyses choices. First of all, it is assumed that the total amount of
cable is kept constant at 6000 feet. This is approximately the same as
the 1900 meter upper limit specified for H1. Also, for networks using
this much cable, we would probably require that the best cable be used.
Therefore, only type A cable is included.
The bit rate is 31.25 kbits/second, which agrees with the present
H1 spec.
Only BUS networks are used. This is based on numerous initial
simulations which show that the BUS network invariably has greater
distortion than the TREE.
Each terminator consist of a 100 ohm resistor in series with a 2
microfarad capacitor. Simulations were done for each of three drop
loads (at end of each drop):
1. 1 picofarad capacitor (to simulate open circuit).
2. A 1000 pf capacitor.
3. A 2500 pf capacitor.
The 1 pf load is used as a reference condition against which to compare
other data. The 1000 pf and 2500 pf capacitances are thought to be
representative of what will actually be used in H1 devices. The 2500
pf violates the existing H1 limit of 3000 ohm at 1.25 Fr. However, it
is included for reference.
Fixed drop lengths of 1 ft., 100 ft., 200 ft., 300 ft., and 400
ft., are used. The 1 ft. drop is used as a reference condition. The
number of drops is set to 10, 15, 20, and 32; depending on the length
of the drops. (Long drop lengths require fewer drops to keep the total
cable length within 6000 ft.)
5. Some Eye Diagrams
Some representative eye diagrams are shown in figures 4 through 8. All of these show only 10 waveforms instead of the 100 waveforms used in the general analysis. Other departures from the conditions stated in section 4 are also included to illustrate extremes.
Figure 4
Figure 5
Figure 6
Figures 4 - 6 are all based on 32 devices, a drop load of 2500 pf, and drop length of 100 ft. Figure 4 used a worst-case gain (abbreviated WG) transfer function. Figures 5 and 6 used worst-case delay difference (WDD) and worst-case gain ratio (WGR) transfer functions, respectively.
Figure 7
Figure 7 is a WG eye diagram that used 32 devices, a drop load of 1
pf, and drop length of 1 ft. This is a reference condition
representing the best that can be done with essentially just the trunk
cable alone. The received amplitude is typically 0.4 to 0.6 of the
transmit (reference) amplitude throughout the diagram.
At the other extreme is figure 8, which is the WGR diagram for 32
devices, 2500 pf drop loads, and 300 ft drop lengths. The total cable
for this particular simulation was increased to 10,000 ft. to
accommodate the large drop lengths. The diagram shows complete eye
closure at some points.
Figure 8
6. Results
The first stage simulations consider 3 different drop loads and 14 different drop length/field device number combinations; for a total of 4200 network constructions. From these, 126 worst-case paths are selected based on the 3 worst-case criteria given above. In the 2nd stage, 100 waveforms are passed through each of the 126 paths; for a total of 12,600 waveforms.
Figure 9
The data is presented in figures 10 through 19 in the form of
minimum eye opening versus number of drops and drop length. The Y axis
value is the minimum eye opening in dB below the transmitted signal.
This is derived as shown in figure 9. Figures 10, 11, and 12 are WG
(worst-case gain) curves for 1pf, 1000 pf, and 2500 pf drop loads,
respectively. Figures 13, 14, and 15 are WDD (worst-case delay
difference) curves for 1 pf, 1000 pf, and 2500 pf drop loads,
respectively. Figures 16, 17, and 18 are WGR (worst-case gain ratio)
curves for 1 pf, 1000 pf, and 2500 pf drop loads, respectively.
Figure 10
WG/C1 Eye Opening Vs # Drops
1 pf load, worst-case gain
Figure 11
WG/C1000 Eye Opening Vs # Drops
1000 pf load, worst-case gain
Figure 12
WG/C2500 Eye Opening Vs # Drops
2500 pf load, worst-case gain
Figure 13
WDD/C1 Eye Opening Vs # Drops
1 pf load, worst-case delay difference
Figure 14
WDD/C1000 Eye Opening Vs # Drops
1000 pf load, worst-case delay difference
Figure 15
WDD/C2500 Eye Opening Vs # Drops
2500 pf load, worst-case delay difference
Figure 16
WGR/C1 Eye Opening Vs # Drops
1 pf load, worst-case gain ratio
Figure 17
WGR/C1000 Eye Opening Vs # Drops
1000 pf load, worst-case gain ratio
Figure 18
WGR/C2500 Eye Opening Vs # Drops
2500 pf load, worst-case gain ratio
For the situations simulated, the attenuation ranges from a low of about 6 dB to a high of 19 dB. Suppose that a 1000 pf load is considered the nominal situation. Then the WG curves (figure 11) have greater attenuation than either WDD (figure 14) or WGR (figure 17). Suppose we want to limit attenuation to 12 dB. Then from figure 11 the acceptable combinations of drop lengths and number of devices are
10 devices, 300 ft.
15 devices, 100 ft.
20 devices, 100 ft.
32 devices, 1 ft.
The WDD data predicts the same combinations. The WGR data predicts almost the same combinations, except that for 15 devices, 200 ft. drop lengths appear to be OK.
7. Comparison With Standard
Annex C of the current Standard has the following:
1 to 12 devices, 394 ft.
13 to 14 devices, 295 ft.
15 to 18 devices, 197 ft.
19 to 24 devices, 98 ft.
25 to 32 devices, 0 ft.
These numbers were derived assuming a 38.4 kbits/second bit rate and with no direct derivation of minimum eye opening. They are based on attenuation and delay distortion derived in simulations similar to those of the stage 1 simulations used here. The new data roughly follows that of Annex C, but is slightly more restrictive. This suggests that the Annex C conditions will produce eye openings of greater than 12 dB below reference.
The Standard currently specifies less than 10.5 dB attenuation between any two devices over the frequency range of 0.25 Fr to 1.25 Fr. As stated in the Standard, this attenuation is the value that would be measured using a sine wave generator. Therefore, it is not the same as minimum eye opening used in the simulations. However, the stage 1 part of the simulations generate worst-case transfer functions over this frequency range. Therefore, worst-case attenuation data is available for all of the network conditions simulated. The attenuation for various selected conditions is given in table Table 1 below.
TABLE 1
NUMBER LOAD DROP WORST-CASE FREQ OF ATTENUATION
DEVICES (pf) LENGTH CRITERION MAX ATTEN (dB)
(ft.) (Hz)
10 1 1 wg 37829.7 5.18844 10 1 1 wdd 26013.8 1.26468 10 1 1 wgr 37829.7 2.10947 10 1000 300 wg 37829.7 6.61848 10 1000 300 wdd 28036.9 4.34874 10 1000 300 wgr 37829.7 6.22010 10 1000 400 wg 37829.7 8.10311 10 1000 400 wdd 32567.3 6.52790 10 1000 400 wgr 37829.7 8.10311 10 2500 300 wg 37829.7 7.45721 10 2500 300 wdd 28036.9 4.63118 10 2500 300 wgr 37829.7 6.99177 10 2500 400 wg 37829.7 9.03194 10 2500 400 wdd 32567.3 6.84938 10 2500 400 wgr 37829.7 8.96561
15 1000 100 wg 37829.7 5.31825 15 1000 100 wdd 28036.9 3.23399 15 1000 100 wgr 37829.7 4.66551 15 1000 200 wg 37829.7 6.69255 15 1000 200 wdd 30217.3 5.07992 15 1000 200 wgr 37829.7 6.22394 15 1000 300 wg 37829.7 8.99871 15 1000 300 wdd 32567.3 7.17377 15 1000 300 wgr 37829.7 8.75540 15 2500 100 wg 37829.7 6.18720 15 2500 100 wdd 26013.8 3.72105 15 2500 100 wgr 37829.7 5.86918 15 2500 200 wg 37829.7 7.40146 15 2500 200 wdd 28036.9 5.59357 15 2500 200 wgr 37829.7 7.36236 15 2500 300 wg 37829.7 9.89252 15 2500 300 wdd 30217.3 7.63898 15 2500 300 wgr 37829.7 9.81237
20 1000 100 wg 37829.7 5.90881 20 1000 100 wdd 28036.9 3.84571 20 1000 100 wgr 37829.7 5.28748 20 1000 200 wg 37829.7 8.02780 20 1000 200 wdd 32567.3 6.40343 20 1000 200 wgr 37829.7 7.89213 20 2500 100 wg 37829.7 7.24218 20 2500 100 wdd 26013.8 4.81659 20 2500 100 wgr 37829.7 6.80074 20 2500 200 wg 37829.7 9.29627 20 2500 200 wdd 28036.9 7.37015 20 2500 200 wgr 37829.7 8.79271
32 1000 100 wg 37829.7 7.24991 32 1000 100 wdd 28036.9 5.02209 32 1000 100 wgr 37829.7 7.17889 32 2500 100 wg 37829.7 9.53652 32 2500 100 wdd 26013.8 6.58590 32 2500 100 wgr 37829.7 9.39462
It is seen from the table that the attenuation is never as great as 10.5 dB. Therefore, the existing network configuration "rule" is satisfied by every network simulated, even though some of these same networks produce eye openings that are unacceptably small.
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