Transient Response of Transmission Lines and TDR/TDT

Transient Response of Transmission Lines and TDR/TDT Tzong-Lin Wu, Ph.D. EMC Lab. Department of Electrical Engineering National Sun Yat-sen University Outlines Why do we learn the transient response of transmission line? Example I Example II Reflection at Discontinuity Resistive discontinuity Reactive discontinuity Termination TDR / TDT fundamentals 1

Why do we learn transient response? (Example: I) Discontinuity can not be avoided in the high speed digital circuits. Example I: 1 Discontinuity 2 3 C equivalent IBIS output model R C SPICE model IBIS input model Why do we learn transient response? (IBIS Model) IBIS (I/O Buffer Information Spec.) Model: Driver Receiver Pull up Pull down Ramp rate Power clamp R_pkg L_pkg C_pkg R_pkg L_pkg Power clamp Gnd clamp C_comp C_pkg Gnd clamp 2

Why do we learn transient response? (Example: I) Experimental setup PCB: 25*3in (L*W), h=.59in, εr=4.5 Battery 5V Clock generator 14.318MHz 74F4D A R C 22 in 74F4D Measuring the driver (A) / receiver(b) output with digital oscilloscope (BW=5MHz) B Why do we learn transient response? (Example: I) Ringing effect simulation measurement driver receiver 3

Why do we learn transient response? (Example: I) simulation measurement driver receiver Why do we learn transient response? (Example: I) simulation measurement driver receiver 4

Why do we learn transient response? (Rule of Thumb) Rule of Thumb: Transmission Line effect should be considered when Length (of transmission) > 1 6 T rise T For example: Rambus 28 Ω signal line, T 17 ps / inch For 2 ps rising edge, Length.49cm!! The reflection effect will occur when the Rambus signal Length is longer than 5mm. Why do we learn transient response? (Example: II) Discontinuity of signal trace (such as stub, via,..) 5

Why do we learn transient response? (Example: II) Discontinuity of signal trace (such as stub, via,..) Signal Spectra of Square Wave Periodic square wave pulse train t t x( t) = a + a cos(2 πn ) + bnsin(2 πn ) T n n= 1 T n= 1 Amplitude: A Pulse width: τ Pulse period: T Aτ a = T A τ an = sin(2 π n ) nπ T DC term A b = τ n [1 cos(2 π n )] nπ T 6

Signal Spectra of Square Wave 5% Duty Cycle Only odd harmonics Reflection at Discontinuity (impedance discontinuity) Reflection Coefficient ' Vr Z Z η = = = Reflection coefficient ' V Z + Z i V t = V + V = ( 1+ η) V i r i 7

Reflection at Discontinuity (open discontinuity) ' Z Z η = ' Z Z = 1 Reflection at Discontinuity (resistive discontinuity) Bounce diagram Voltage Transient response at the source end Voltage Transient response at the load end Current Transient response at the source end Current Transient response at the load end 8

Reflection at Discontinuity (reactive discontinuity) Concept Transient step response of a inductor Reflection coefficient is depend on frequency When steady state (DC), inductance acts like a short. Reflection at Discontinuity ( capacitive reactive discontinuity) Rising edge Equivalent circuit for Z transmission line The maximum reflected noise by the capacitance Reflection waveform by a small shunt capacitance V r CZ = 2T V T r : Rise time of the input step signal r 9

Reflection at Discontinuity ( capacitive reactive discontinuity) Theory Equivalent circuit for Z transmission line Vr Z η = = V Z Z Z Z ZL =( jωc// Z ) = 1 + jωcz jωcz V = + jωcz V r 2 Assume jωcz 2 L L CZ Vr 2 ( jωv ) In time domain, CZ d v t dt v t r () ( ()) 2 CZ The maximum noise V = T V r 2 at the rising edge r Reflection at Discontinuity ( capacitive reactive discontinuity) Theory Like a triangular area It can be proved that the total area under the curve is area = CZ T V T C Z 1 2 r = V 2 2 2 r It is independent on the rise time!! 1

Reflection at Discontinuity ( inductive reactive discontinuity) Equivalent circuit for Z transmission line The maximum reflected noise by the inductance L V = Z T V r 2 r T r : Rise time of the input step signal Total Area is Reflection waveform by a small series inductance A = L V 2Z TDR signatures produced by simple discontinuities 11

Termination Parallel termination Termination to Ground Termination to Power Vcc R R Thevenin termination Termination to Voltage V T R1 Rd R2 Vth R Termination Parallel termination Termination to Ground Termination to Power Vcc R R Design Equation: R= Design Equation: R= Advantages: Simplest Disadvantage Power consumption Cost R elements and PCB space Which one is better if you have to choose one? 12

Termination Parallel termination Thevenin termination R1 Design Equations: Keep I oh and I ol within spec Rd R2 Vth V th =V oh (min)-i oh (max)(r d +Z o ) R 1 // R 2 =Z o Advantages: Balanced Disadvantage Static Power consumption Cost R elements and PCB space R 1 =Z o V cc /V th R 2 =Z o V cc /(V cc -V th ) Termination Parallel termination Termination to Voltage V T R Design Equation: R=Z o Advantages: Less static power consumption Disadvantage Static Power consumption Cost R elements and PCB space 13

Termination Parallel termination DC current path for totem pole driver Termination Parallel termination Power consumption and DC current 14

Termination Parallel termination Voltage swing To obtain the maximum noise margin, the widest noise swing is required The maximum swing is got when R << Z. But it will cause a large reflection at source and high power dissipation. Termination AC termination Rd R C Advantage: Power saving Disadvantage: Data line may exhibit time jitter (depend on previous pattern) C is not easy to design Application Battery-driven systems 15

Termination AC termination Termination diode termination D1 Vcc The V(out) is limited to Vcc+Vt to -Vt Rd D2 Vt : threshold voltage of the diode Advantage: Require no matching (large impedance variation) Lower power dissipation Standard ESD protection circuit include diode clamping in the configuration identical the diode termination Disadvantage Existence of multiple reflection 16

Termination diode termination Termination series termination R Rd Design Equation: R=Z o -R d Advantages: Simple Consume less power Disadvantage The R d is different for Pull-up and Pull-down Reduce noise immunity in a multi-drop bus situation (such as clock chain) Because of half voltage is launched into the transmission line) 17

Termination series termination Termination In practical design, which one is better? 1. None 2. Series 3. AC 4. parallel 18

Time Domain Reflectometry Bandwidth : 2GHz Min. rising time: 38ps Calibration of error in TDR measurement is quite important Time Domain Reflectometry (Calibration) Before accurate impedance measurements can be performed, the frequency response errors and losses caused by the imperfections in the system, cables, and probing hardware must be removed by the calibration. Procedures: 1. Short 2. Load (5 ohm) 3. Open 19

Time Domain Reflectometry (Calibration) Principles of calibration Measured waveform in TDR Errors (cables, connectors, probes) Device under test TDR measurement (Impedance Profile measurement) 2

TDR measurement (Parasitic capacitance measurement) Discrete shunt capacitance The voltage distribution v.s. time at point H Reflected wave Transmitted wave TDR measurement (Parasitic capacitance measurement) The equivalent circuit at point H = (Z // Z ) The transmitted wave at point H = V / 2 V t / VH () t = ( e ) 2 1 τ = RC = Z where τ C 2 V VH() t = + Vref () t 2 = Incident wave + Reflected wave = Transmitted wave The reflected wave is V V t e t / τ () = ref 2 21

TDR measurement (Parasitic capacitance measurement) z V A t dt e t V V Z = V ref () = / τ dt = τ = ( C ) 2 2 2 2 z C = ( 2 A) 2 Z V TDR measurement (Parasitic capacitance measurement) TDR signature by HP TDR/TDT Capacitance effect Capacitance value 22

TDR measurement (Parasitic inductance measurement) Reflected wave Transmitted wave TDR measurement (Parasitic inductance measurement) Equivalent circuit seen between J and K The transmitted wave at point J V t V j = + e 2 1 / τ ( ) V t Vk = e 2 1 / τ ( ) L where τ = L = R 2Z The reflected wave is V e t 2 /τ 23

TDR measurement (Parasitic inductance measurement) Inductance signature Inductance value 24