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2.5 Reflection of DC voltage in Transmission lines 69 2.6 "Long" and "Short" Transmission Lines As we have seen in section 2.2, if a circuit handles low-frequency AC power, the short time delays between source and load voltages introduced by a transmission line are of little consequence. This is because, since line-length propagations occur within a very small fraction of the AC waveform's period, the actual phase difference between start-of-line and end-of-line signals is negligible (Figure 2.2-2). In these cases, we can say that the transmission lines in question are electrically "short", because their propagation effects are much quicker than the periods of the signals they carry. By contrast, an electrically "long" line is one where the propagation time is a large fraction or even a multiple of the signal period. A long line is generally considered to be one where the source's signal waveform completes at least a quarter-cycle (90⁰ phase increment) before the incident signal reaches the end of the line (Figure 2.2-5). To allow us to make the distinction between long and short lines more easily, we introduced the concept of wavelength in section 2.2 (page 30). A line is considered long if it is at least in length. For a 50 Hz AC power system, power lines would have to exceed 1500km in length before the effects of propagation time became significant. Cables connecting an audio amplifier to speakers would have to be over 7.5km in length before line reflections would significantly impact a 10 kHz audio signal! When dealing with radio frequency systems however, the lengths of transmission lines have a much greater influence on the operation of the circuit. Consider a 100 MHz radio signal: its wavelength is 3m if the signal is propagating at the speed of light. This means that even a line which is 60-75cm in length would be considered long. If the propagation velocity of the line is lower, it would be considered long for even shorter lengths. For instance if our line was characterised by a velocity factor of 0.66, this critical length would shrink to 50cm. The fundamental difference between short and long transmission lines may be summarised by two points: - When an electrical source is connected to a load via a short transmission line, the load's impedance dominates the circuit. - When a source is connected to a load via a long transmission line, the line's own characteristic impedance dominates over the load impedance in determining the circuit behaviour. In other words, an electrically long line acts as the principal component in the circuit and its own characteristics have greater influence than the load. The most effective way to minimize the impact of the length of a transmission line on circuit behaviour is to match the line's characteristic impedance to the load impedance. If the load impedance is equal to the line impedance, then any signal source connected to the other end of the line will see the exact same impedance, and will have the exact same amount of current drawn from it, regardless of the length of the line. In this condition of perfect impedance matching, the length of the line only affects the time it takes the signal to reach the load. However, perfect matching of line and load impedances is not always practical or possible. We will see the effect that different terminations have on the behaviour of high frequency circuits in section 2.8 but we will start by looking at a simple example in the next section (2.7). Conquer Radio Frequency 69 www.cadence.com/go/awr

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