# Impedance mismatch and solutions

Before matching the impedance, a few terms are introduced to you.

Transmission line: consists of two wires of a certain length, e.g. coaxial cable, microstrip wire, ribbon wire (copper alignment in a PCB board), etc.

Uniform transmission line: If the cross-section of the wires is the same everywhere, e.g. coaxial cable, the transmission line is uniform, i.e. the impedance is equal everywhere.

Transient impedance: When a signal is transmitted on a transmission line, the impedance of the current passing through each place is the transient impedance, which is constant for a uniform transmission line when the materials are the same and the cross-sectional area is the same.

Characteristic impedance: For uniform transmission lines, the instantaneous impedance is the same at any point when the signal is propagated on it, and this instantaneous impedance is called the characteristic impedance of the transmission line.

Transmission line time delay TD: commonly understood as the signal from the source of the transmission line to the end of the time used

With the above basic concepts out of the way, let’s get down to business.

We all encounter a lot of overshoot, undershoot and ringing phenomena in testing signal waveforms, all of which are problems of signal integrity. Of course, the reason for these phenomena is the impedance mismatch, as there are reflected signals bouncing back and forth.

Examples of impedance mismatch phenomena are shown in Figure 1.

Figure 1

Then I would like to ask you: why is there a reflected signal?

The fundamental reason: in order to maintain the equilibrium of the system, there cannot be a voltage discontinuity at the boundary, otherwise there would be an infinite electric field, nor a current discontinuity, otherwise there would be a net charge generated out of the intersection first.

In Figure 2 below.

Z1: impedance on the left Z2: impedance on the right

Vinc:incident signal

Vtrans:transmitted signal across the intersection

Vrefl:reflected signal

where ρ is the reflection coefficient

Figure 2

A signal that encounters an impedance mismatch during transmission, as in Figure 2, results in a reflected signal, with part of the incident signal passing through the mutation into Z2 and part reflected back to the source.

The condition that the voltages on both sides of the intersection are the same is: Vinc + Vrefl = Vtrans

The condition that the currents on both sides of the interface are the same is: Iinc – Irefl = Itrans

Then why I mentioned above: when there is a sudden change in impedance, why there is a reflected signal, we use the formula to prove

For a moment.

If no reflected voltage is generated and the voltage and current are to be kept continuous, wouldn’t V1=V2 and I1=I2

Z1=V1/I1 and Z2=V2/I2, so if there is a sudden impedance change, i.e. an impedance mismatch, then Z1≠Z2, is V1 still equal to V2 and I1 still equal to I2? Obviously, they are not equal. In order to continue to maintain this system balance, there is a reflected voltage.

Above I have explained clearly why the ringing occurs and why the reflected signal appears.

I would also like to give you a schematic analysis of why the sudden high and low waveforms in Figure 1 occur.

Let me first give you a bounce diagram, as in Figure 4.

Figure 4

10R in Figure 4 is the internal resistance of the driver. Our common drivers are generally TTL circuits internally, which have a very small internal resistance or output resistance, typically a dozen ohms.

Figure 4, 50R is the characteristic impedance of the transmission line, that is, the impedance of the transmission line is 50R everywhere

R=-0.67 in Figure 4 refers to the reflection coefficient R=10-50/10+50=-0.67 when the signal is reflected from the end back to the source.

R=1 in Figure 4, this figure shows that we have not added any terminating resistors and the end is understood as an open circuit, i.e. the impedance is infinite.

R=infinity/infinity=1, i.e. total reflection.

Our incident signal is 1V, i.e. the signal amplitude at point A is 1V, the signal will be reflected after going from point A to point B, because there is a sudden change in impedance at point B. The transmission line is 50R and the termination is infinity, so total reflection occurs, then the voltage at point B = incident signal + reflected signal, where the reflected signal is 1V*R (R=1) = 1V and the incident signal is 1V, then the first occurrence at point B voltage is 2V.

The reflected signal 1V at point B returns to point A and then encounters an impedance mutation, because the driver internal resistance 10R and transmission line 50R are not equal, then the voltage reflected back to point B is: 1V*(-0.67)=-0.67V, -0.67V voltage will again go to point B, where it encounters an impedance mutation and a total reflection, -0.67V is reflected back to point A, then the voltage at point B at this time is Vb = 2V before + reflected voltage + incident voltage = 2 – 0.67 – 0.67 = 0.66V and so on.

If you draw the waveform at point Vb in time-amplitude coordinates, you will see why the ringing is a high and low waveform. It is this reflected signal that is the cause.

So next I will tell you how to solve this phenomenon when it occurs, or how there are usually several solutions.

Layou engineer solution + hardware engineer solution

Layout engineers can optimize as much as possible under the premise of: alignment as little as possible when punching holes and layer alignment, because punching holes, there will definitely be impedance mismatch, and alignment as far as possible to go Fly-by or daisy chain topology type of alignment. See Figure 5

Figure 5

Daisy chain alignment or Fly-by alignment disadvantage is that it is not easy to do equal length, such as DDR alignment, T-type easy to do equal length, this will need to choose according to their actual problems.

Alignment do not appear right angle, sharp angle, why this can not be done, these two ways of alignment, in the corner will certainly appear impedance mismatch, we draw on paper is easy to understand, as a junior high school maths problem.

Termination resistors: there are five kinds (source series termination, terminal parallel termination, Davinan parallel, RC termination, diode termination). The ones I use more often in my work are series terminated at the source, RC terminated, and diode terminated. We are probably the most commonly used is in fact the first, the next issue to tell you about these five termination methods, their respective characteristics and applications.

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