22.214.171.124.4. Using Parallel Termination
- A 300-ps rise-time signal
- Two-inch long transmission path between the source and the destination
- delay = 85√εr ps per inch
- delay = 85√(0.457εr+0.67) ps per inch
- V = VFINAL(1–e–t/RC)
- 0.1 VFINAL = VFINAL (1–e–t1/RC)
- 0.9 = e–t1/RC
- 9 = e(t2–t1)/RC
- ln 9 = (t2–t1)/RC
- 2.197 = (t2–t1)/RC
- t2–t1 = Rise time of the signal (Tr) and RC = time constant = r
- Frequency = 1/2 πr
- r = RC = 1/2 πf
- 2.197 = 2 πf Tr
- f = 0.35/Tr
- Bandwidth = 0.35/Tr
- Bandwidth = 0.35/300 ps = 1.16 GHz
- Speed = Frequency x Wavelength
- 5.5 giga inches per second = 1.16 GHz x wavelength
- wavelength = 4.74 in.
- wavelength/10 = 0.474 in.
- Reflection coefficient = (ZLOAD – Z0)/(ZLOAD + Z0)
Time Domain Reflectometry
Time domain reflectometry (TDR) is a way to observe discontinuities on a transmission path. The time domain reflectometer sends a pulse through the transmission medium. Reflections occur when the pulse of energy reaches either the end of the transmission path or a discontinuity within the transmission path. From these reflections, the designer can determine the size and location of the discontinuity. This section provides an understanding of TDR.
Figure 45 shows a TDR voltage plot for a cable that is not connected to a PCB. The middle line is a 50-Ω cable one meter long. At point A, a pulse starts (Z0 = 50-Ω) and transmits through the cable, stopping at the end of the transmission line (i.e., Point B). Because the end of the transmission line is open, there is infinite impedance, ZLOAD = α. Therefore, the reflection coefficient at the load is determined with the equation:
The entire signal is reflected. At point B, the amplitude of the signal doubles. Refer to Figure 45.
If the same meter-long cable is then connected to a PCB through an SMA connector, the plot changes. Refer to Figure 46. Because the SMA connector is more capacitive than inductive in nature, it appears as a capacitive load, shown as a dip in the TDR plot.
Figure 47 shows an expanded curve for the SMA connector. Because the rise time of the pulse sent for TDR analysis is very small (around 20 ps), the TDR voltage plot shows every discontinuity on the transmission path.
The SMA is a capacitive discontinuity on the transmission path, so the signal dips on the voltage plot. The impedance of an ideal transmission line is defined by the following equation:
Therefore, when the capacitance increases, the impedance decreases. If the discontinuity is inductive, then the impedance increases, which appears as a bump in the TDR plot. You can calculate the capacitance and inductance from the curves on a TDR plot. If the plot shows a dip, as in Figure 47, then calculate the capacitance.
The equivalent circuit approximation for a dip in the TDR plot is a capacitor to ground, as shown in Figure 48.
The RC equation for this type of circuit is:
The two transmission lines behave as if they are parallel to each other.
You can determine the change in voltage (ΔV) and rise time (Tr) from the curve. Then, you can enter the values into the equation (i.e., Z0 = 50 Ω):
Use this equation to determine the RC time constant. You can also use the curve to approximate the RC time constant. Between 0 to 63 percent of the rise is RC. Once the RC is found, you can use it to determine the capacitance (discontinuity, as seen by the signal).
If the discontinuity looks more inductive in nature (i.e., the curve goes up), then the signal experiences a circuit similar to Figure 49. The transmission line is split, with an inductive discontinuity in between.
Use the following two equations to find inductive discontinuity (L):
To determine the inductance value, use the equation for (Z0 = 50 Ω):
Figure 50 shows a cross section of a PCB transmission path, which illustrates many discontinuities.
If you experience a TDR plot similar to Figure 51, calculate the capacitive discontinuity introduced by the SMA connector by factoring in the voltage dip.
You can determine Tr and V for the equation from the curve as shown in Figure 52.
In this example,
From the equation:
The examples in this section can be used when modeling discontinuity with a simulator. However, instead of using TDR to extract the parasitic for the discontinuity, you can model the discontinuity in the 2D and 3D field solvers.
Reflection coefficient = (ZLOAD – Z0)/(ZLOAD + Z0)
Reflection coefficient in this case = (α– 50)/(α + 50) = 1
Z0 = √(L/C)
R = Z0/2
RC = Z0C/2
(ΔV/250 mV) = 1 - (Tr /2RC)
R = 2Z0
L/R = L/2Z0
(ΔV/250 mV) = 1 - (Tr x Z0 /L)
(ΔV/250 mV) = 1 - (Tr /2RC)
RC = (Tr x 250 mV)/2 (250 mV - ΔV) = 29.9 ps
RC = Z0C/2
If Z0 = 50 Ω, then C = 1.196 pF
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