- How does a TDR find cable distance?
- A voltage step travels down the cable at v = velocity factor times c. The first echo returns after t = 2L/v, so the apparent distance is L = vt/2.
- Why do open and short circuits reflect with opposite signs?
- The load reflection coefficient is Γ = (ZL - Z0)/(ZL + Z0). An open circuit has Γ ≈ +1, so the voltage step reflects upward; a short has Γ ≈ -1, so it reflects downward.
- Why is a matched load (Z_L = Z₀) desirable?
- A matched load results in a reflection coefficient of zero (Γ=0). This means all power delivered by the source is absorbed by the load, with no reflected wave. This maximizes power transfer, eliminates standing waves (resulting in a flat voltage magnitude along the line), and prevents signal distortions and potential damage to the source amplifier in high-power systems.
- What does a purely imaginary load impedance (e.g., Z_L = jX) represent physically?
- A purely imaginary impedance represents a reactive load—either a capacitor or an inductor—with no resistive component to dissipate power. Such a load reflects 100% of the incident power (|Γ|=1), creating a perfect standing wave. The phase of Γ, and thus the position of the voltage minima, depends on whether the reactance is inductive (positive) or capacitive (negative).
- The simulator shows a standing wave for a mismatched line. Does this mean the voltage at a point isn't changing with time?
- No, the voltage at any point is still sinusoidal in time. The 'standing wave' refers to the envelope of the oscillation. While the wave oscillates everywhere, the *amplitude* of that oscillation varies with position. At a voltage maximum, the oscillation swings between large positive and negative values; at a node (minimum), the amplitude is very small or zero.
- What is a key limitation of this simplified model?
- This model assumes a lossless and dispersionless line, meaning signal attenuation and frequency-dependent propagation effects are ignored. Real transmission lines have finite resistance and conductance, causing the standing wave pattern to diminish in amplitude with distance from the load. It also models a single frequency, whereas real signals contain a spectrum of frequencies.