# TEXAS INSTRUMENTS' Electronic Mail message # 171179

Kevin Gingerich S=Kevin_Gingerich%S=Gingerich%G=Kevin%TI at mcimail.com
Thu Oct 6 04:52:00 PDT 1994

To  SCSI Reflector   X400

>From  Kevin Gingerich  GING

Apparently Word 6.0 decided to change 'straight quotes' to 'smart quotes' for
me and some prime (') marks were lost in the translation. A corrected version
follows. /Kevin/

******

The SCSI bus is a distributed parameter circuit whose electrical
characteristics and responses are primarily defined by the distributed
inductance and capacitance along the physical media. The media is defined here
as the interconnecting cable(s) or conducting paths, connectors, terminators,
and SCSI devices added along the bus. The following analysis derives a
guideline for the amount of capacitance (and its spacing) that can be added to
the Single-ended Fast-20 SCSI bus.

To a good approximation, the characteristic transmission line impedance seen
into any cut point in the unloaded SCSI bus is defined by Z = SQRT(L/C), where
L is the inductance per unit length and C is the capacitance per unit length.
As capacitance is added to the bus, in the form of devices and their
interconnection, the bus impedance is lowered and can be expressed by Z' =
SQRT(L/(C+C')), where C' is the added capacitance per unit length. When
capacitance added to the bus by devices, an impedance mismatch occurs. When a
signal wave arrives at this mismatch in impedance, an attenuation (or
amplification) of the signal will occur. The magnitude of the attenuation will
depend upon the ratio of the mismatched impedance or A = Z'/Z, where Z' is the
load impedance and Z is the source impedance.

Substituting the equations for Z' and Z and reducing,

1)   A = Z'/Z = SQRT(L/(C+C')) = SQRT(1/(1+C'/C)).

We now have a relationship for the attenuation of the signal voltage at an
impedance mismatch due to load capacitance distributed on the SCSI bus. Next, a
rule for the ratio of Z' to Z will be derived.

With fast transfer rates and electrically long(1) media, it becomes essential
to achieve a valid input voltage level on the first signal transition from an
output driver anywhere on the bus. This is called incident-wave switching. If
incident-wave conditions are not achieved, reflected-wave switching must be
used. Reflected-wave switching depends upon reflected energy occurring some
time after the first transition arrives to achieve a valid logic voltage level.
In the Fast-20 SCSI environment, the valid low-level input voltage threshold
has been raised and the high-level input voltage threshold has been lowered to
allow incident-wave switching with some inevitable impedance mismatching and
signal attenuation along the media.

The signal voltage at an impedance mismatch is VL1 = VLO+VJ1+VR1, where VL0 is
the initial voltage, VJ1 is the input signal voltage, and VR1 is the reflected
voltage. The voltage reflected back from the mismatch is VR1 = pL x VJ1 where,
pL = (Z'-Z)/(Z'+Z) and is the coefficient of reflection commonly use in
transmission line analysis. The voltage equation can now be written as VL1 =
VL0+VJ1+pL x VJ1.

When a SCSI signal is asserted, the VL0 can be at a maximum of 3.7 V and go to
0 V (for a perfect driver) giving a VJ1 of -3.7 V and the signal voltage must
go below the minimum receiver input voltage threshold of 1 V. In equation form,

1>3.7+(-3.7)+pL x (-3.7)
pL>(1-3.7+3.7)/(-3.7) = -0.27

The negative value means that no more than 27% of the input signal voltage can
be reflected back towards the source or the minimum assertion level will not be
achieved by the incident wave(2).

Now, to relate this to Z'/Z and using equation 1) for C'/C,

2) pL = (Z'-Z)/(Z'+Z)>-0.27
Z'-Z>-0.27(Z'+Z)
Z'(1+0.27)>Z(1-0.27)
Z'/Z>0.73/1.27 = 0.57

and

0.57<SQRT(1/(1+C'/C))
1/(0.57^2)-1>C'/C
C'/C<2.08

We can now say that capacitance should not be added at more than twice the bus
distributed capacitance for incident-wave switching. For example, a cabled bus
with L = 295 nH/m (90 nH/ft) and C = 41 pF/m (12.5 pF/ft) and Z = 85 ohms, the
guideline becomes to add no more than 85 pF/m (26 pF/ft) anywhere along the
bus. This guideline can be met by 25 pF loads spaced 0.3 m (1 ft) from each
other, 50 pF spaced 0.6 m (2 ft) apart, or 12.5 pF spaced 0.15 m (0.5 ft)
apart. This relationship is shown graphically in figure 1.

Figure 1. Minimum device spacing versus bus and device capacitance.
_______________________________
(1)Electrically long is defined here as td>tr/3, where td is the one-way time
delay across the bus and tr is the 10% to 90% transition time of the fastest
driver output signal.
(2)A similar analysis can be used for the negation case of 0 V to 2.8 V ([48 mA
+ 22 mA] x 40) and an input voltage threshold of 1.9 V for a minimum reflection
coefficient of -0.32. This leaves assertion as the most restrictive case.