lecture 7 photonic signals and systems an...

Lecture 7

Photonic Signals and Systems- An Introduction

- By- Nabeel A. Riza *

04/10/2019 N. A. Riza Lectures 1

• Text Book Reference: N. A. Riza, Photonic Signals and Systems – An Introduction, McGraw Hill, New York, 2013.

Lecture 7 Overview

Topics:

Two conditions required to enable EM waves interference – i.e., Having at least two EM waves

overlapping in a region and an EM wave detector operational in this overlap region.

Physical and Mathematical representation of Interference in the RF regime of the EM spectrum

with EM detector (RF antenna) implementing RF interference by producing an electrical current

that is proportional to the sum of the E-fields (e.g., sum of sinusoids ) of the incident RF waves .

Physical and Mathematical (i.e., amplitude and RF phase conditions needed) representation of

Constructive and Destructive Interference in the RF regime of the EM spectrum.


Introduction to InterferenceThe interference phenomena is common when using radio-wave equipment, such as mobile/cell phones and satellite television.

During electrical storms, the TV picture can deteriorate with snowing or completely losing the video signal.

Similarly, while walking in a busy downtown with many tall buildings and heavy cell-phone traffic, cell-phone users can pick up unwanted audio chatter or simply have their audio signal fade away and disconnect (see Figure 4.1).

Even advanced electronic systems like radars in airport air-traffic control, weather reporting, military-aircraft guidance, and missile targeting can experience the effect of interference. These are examples of annoying interference or, more specifically, interference in the radio band of the EM-waves spectrum.

Complementary Slide


Introduction to InterferenceComplementary Slide


RF and Light Interconnection

Figure 4.2 shows a flowchart linking RF and optical-wave behaviour within electronic- and optical-hardware context and its required interference conditions.

EM waves in a linear infinite-transmission media like air, metal, glass, and silicon, will not interact or engage with another EM wave flowing in the same medium.


Interference of EM Waves

As shown in Figure 4.3, EM Wave A will not interfere with EM Wave B, and both waves will continue to flow unperturbed in the medium.

The act of interference occurs when we actually try to “observe” or “capture” these waves at a physical location where the two waves spatially overlap.

Specifically, this happens when we place an EM-wave detector in this overlap region so the EM-wave detector can simultaneously respond to the presence of both Waves A and B.


Interference in the RF Regime of the EM Spectrum

To observe, measure, or witness RF interference, we must deploy the EM detector called the RF antenna in the physical path of the incident EM waves. Specifically, the RF antenna circuit produces a current flow or voltage oscillation at the given frequencies of the incident radio signals.


Interference in the RF Regime of the EM SpectrumNeed for Plane Wave fronts

It is assumed that the EM wave fronts that fall along the length of the antenna are plane wave fronts (see Figure 4.5) along the same wave propagation direction, an important physical wave attribute needed for high-quality or high-coherence interference over the RF antenna structure.

If this were not so, a spatially varying relative phase between the two interfering EM waves exists over the antenna structure that on average washes out the antenna-detected interference signal.

For the interference studies presented in this chapter, the ray optics model holds, in other words, plane wave fronts are assumed to arise because of ray or straight-line EM-wave propagation.


Interference in the RF Regime of the EM SpectrumE-Field Representation

Each traveling-wave electrical field in units of volts/meter produces an equivalent voltage in the antenna wire; for example, VA ∝ EA and VB ∝ EB. More specifically, VA = GaEA and VB = GaEB, where Ga can be called the antenna gain figure in units of 1/m.

The electric fields are oscillating up and down along the antenna-wire direction as two time-synchronized (or mutually coherent) temporal sinusoids at the RF of fRF. Note that it is also possible for the EM Waves A and B to have different oscillation frequencies. The real electrical-field signals of the EM waves can be written as

where [EA0, φA] and [EB0, φB] are the signal-amplitude phase values for the electric fields EA(t) and EB(t), respectively. These EA(t) and EB(t) electric fields cause conduction electrons in the antenna metal wires to flow and produce electric currents iA(t) and iB(t), respectively.


Interference in the RF Regime of the EM SpectrumE-Field Representation

Hence, the RF voltage signal produced by the antenna detector with two impinging EM Waves A and B can be written as

where the voltage amplitudes are VA0 = GaEA0 and VB0 = GaEB0. Note that the EM-wave relative phases are preserved by the linear antenna detector and this phase information can provide mechanisms for powerful signal processing of incident EM waves. Without loss of generality, we can write φA = 0, thus defining a time-reference position. In the simple case when VA0 = VB0 = V0, we can write

Via the linear transformation of Ohm’s law in the antenna circuit, the RF signal addition or interference is implemented as


Interference in the RF Regime of the EM SpectrumConstructive Interference

It is possible that the EM waves have a relative time delay that satisfies the condition where φB = n2π with n = 0, ± 1, ± 2, …, ± N, where N is an integer.

In effect, the EM Wave B relative-time delay compared to Wave A that satisfies τB = n(1/fRF) = nTRF , where TRF is the time period of the sinusoidal RF signal.

Under these special interfering waves condition, the antenna generates the stronger RF signal as shown in Figure 4.6 to be


Interference in the RF Regime of the EM SpectrumConstructive Interference

Notice that the received signal has an amplified voltage value of VA0 + VB0. Depending on the application, this amplification can be a good thing or a bad thing.

This condition of relative time delay or phase between the interfering EM waves is called the positive interference or constructive interference condition because the gain factor in the summed signal is detected


Example RF system using constructive interferencePhased Array Antenna (PAA)


Interference in the RF Regime of the EM SpectrumDestructive Interference

Opposite to constructive interference, it is also possible that the interfering EM Waves A and B on the RF antenna have a relative time delay that satisfies the condition where φB = (n+1/2)2π with n = 0, ±1, ±2, …, N, where N is an integer.

In effect, the EM Wave B relative time delay compared to Wave A that satisfies τB = (n+1/2)(1/fRF) = (n+1/2)TRF , where TRF is the time period of the sinusoidal RF signal.

Under these special interfering waves condition, the antenna generates the weaker RF signal as shown in Figure 4.8 to be


Interference in the RF Regime of the EM SpectrumDestructive Interference

If the strengths of the two EM waves are the same, in other words, if VA0 = VB0, then the antenna-produced RF signal disappears or v(t) = 0.


Example RF system using destructive interferenceRF-jammer using Phased Array Antenna (PAA)


Problem

Solution


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