11/22/2004 EE 42 fall 2004 lecture 35 1

Lecture #35: data transfer

• Last lecture:– Communications synchronous / asynchronous – Buses

• This lecture– Transmission lines

11/22/2004 EE 42 fall 2004 lecture 35 2

Transmission Lines

• Light travels one meter in approximately 3 nanoseconds. (c=3x108 meters per second in air or in a vacuum)

• When rise times are comparable to propagation times, then Transmission line effects become important.

• Transmission line effects are already important for USB, Ethernet, Personal computer busses.

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Long signal paths

• Signal delay– Component delay + interconnection delay

• Signal integrity• Reflections• Waveform distortion• Signal attenuation• Crosstalk

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Gate delay

• So far, the only delay that we have considered is the time needed to charge up the capacitance due to lines, and due to the capacitance of the gates of the next stage.

• This implies that if we could only push enough current, we can make the delay as short as we like.

Wire Gates

R

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Gate delay

• If we want to speed up logic, we can increase the drive – reduce the pull up and pull down resistance

• or we can reduce the capacitance.– Shorter lines, narrower lines, reduced

dielectric constant of dielectric between wires.

This is limited, however by the speed of light

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Light speed

• With lines that are long enough, or switching speeds are high enough, then we can not consider the delay to be simply that due to charging up the capacitance. The signal will propagate along a wire at the speed of light (in the dielectric, which is slower than that in air or vacuum)

• Quite a bit of current is necessary to pull up a line that fast, for a 1 volt signal, 10-20 milliamps are required.

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Inductance of wire

• The reason that transmission can not be sped up past a certain limit is due to the fact that pushing current through a wire creates a magnetic field.

• This means that the conductors used for communications have an inductance which the current must be driven through.

• If changes in current are slow, or the path is short, this can be neglected, but for high speed communications it dominates

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Inductor

Inductor:

dt

dILV

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Transmission line model

• To properly account for the inductance of the wires in a communications link, we need to put in the distributed inductance and capacitance all along the wires

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Transmission line model

• Why do we need both the signal wire and the return path?

• Because a small loop has much more inductance than a small loop, so the return path needs to be kept very close to the signal wire.

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Differential pair

• The return path can be made by running a wire close to the signal wire, and carrying the opposite voltage and current,

+V

-V

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Ground plane

• Or the return path can be made close to the signal wire by providing a ground plane under all of the signal wires,

B

D

A

C

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Transmission Line

• When a signal wire is driven with that fast a rise time compared to its length, a signal will travel along the wire at the speed of light in the media.

• It is even possible to turn off the current, and have the pulse that is already on the line continue to propagate toward the destination

• So you don’t have to wait for one bit to arrive before you send the next

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Transmission Line

• As the voltage pulses propagate down the line, there is a current pulse which travels down the line with them.

• The current is always in both conductors, for example forward in one conductor, and backward in the other

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Transmission Line

• Voltage

• Current in (+) signal line

• Current in (-) signal line, or current in ground

• If the signal is conducted in a pair of lines, it is called a balanced line. If the return path is through a ground, it is called unbalanced

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Coax

• Coax (coaxial) line is an unbalanced transmission line. The central wire carries the single ended signal, and the shield is attached to ground, and carries the return current.

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Twisted pairs

• One wire in each pair carries +signal voltage and current. The other wire carries the current in the opposing direction, either by being connected to ground, or by being driven by -signal

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Ribbon cable

• Ribbon cable is inexpensive to make, and to connect. It is used by running balanced signals (+V and –V) on adjacent wires, or by grounding every other wire to provide isolation and a current return path

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Strip line

http://www1.sphere.ne.jp/i-lab/ilab/tool/s_line_e.htm

In a PC (printed circuit) board high frequency lines are run in between ground planes, which creates an unbalanced transmission line called a strip line.

The wider the metal trace, the lower the impedance of the transmission line. Impedances are typically 50-100 ohms.

Try out an impedance calculator:

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Transmission line impedance

• The ratio of the voltage of propagating pulses to the current the carry is a constant, called the impedance of the line

• A typical transmission line impedance is 50-100 ohms.• When a line is being used in this fashion, it can not be

split into two, because for a given voltage, twice as much current would be needed

• So digital transmission lines do not branch, there is only one path from one end to another.

pulse

pulse0 I

VZ

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Transmission line formulas

• If a transmission line has the same cross section from one end to the other, then propagation on it can be written:

),(),(

)/()/(),(

)/()/(),(

12

0

0

0

01

00

xtIxtI

vxtfZ

Vvxtf

Z

VxtI

vxtfVvxtfVxtV

Where t is time, and x is distance along the line

11/22/2004 EE 42 fall 2004 lecture 35 22

Transmission line termination

• Since a transmission line carries pulses of voltage and current, there must be somewhere for the current to go.

• FET devices are very high impedance, so they don’t absorb that current

• All that is required to absorb the current at the end of the transmission line is a resistor which has the same resistance as the impedance of the line Rtermination=Z0

• If a termination is not provided, then a reflection will be created, propagating back up the line