Generalized Block Diagramof a Communication system
The SPECTRUM of a SIGNALHOW MUCH “SINUSOIDS” are present in that signal ?→ The theoretical Origin is FOURIER Theory in mathematical analysis: “Any signal can be DECOMPOSED into SUMS of SINUSOIDAL signals”
Types of Signals• Base-band: Its Spectrum is concentrated AROUND f=0.Example: Voltage at the output of a handset• Band-Pass: Its Spectrum is translated FAR from f=0 (around a CARRIER)Example: Voltage from the Low Noise Block of a Dish
Base Band: Telephone Voice Channel
What is “MODULATION”
AM of A CARRIER
Modulation Index “m”
Frequency and Phase Modulation
Modulation index of FM Signal
Mathematical ToolAny Bandpass signal may be represented as: v(t ) R(t ) cos c t (t ) or: v(t ) x(t ) cos( c t ) y(t )sin( c t )or in a Complex form: j g (t ) j (t ) g (t ) x (t ) jy(t ) g (t ) e R (t )e Where : R (t ) g (t ) x 2 (t ) y 2 (t ) 1y (t ) (t ) tan ( ) x (t )
Modulated SignalThe SOURCE of information (Modulating signal orBaseband signal) m(t) is ENCODED into a Bandpasssignal (Modulated signal) s(t) given by: j ct s(t) Re g(t)e
Generalized Transmitter AM-PM technique
Generalized Transmitter Quadrature Technique
Side Bands of AM Signal
Power of AM SignalDelivered to a resistive load
Visualization in the Time and Frequency DomainsThe spectrum analyzer is to the frequency domain as theoscilloscope is to the time domain. It can also be used in thefixed-tune mode (zero span) to provide time-domainmeasurement capability much like that of an oscilloscope.
Time Domain Signal SPECTRUM (Frequency Domain)
Need for DECIBELS 0.001
SMALL and LARGE Signals on the SAME Scale
Types Of Spectrum AnalyzersThere are two basic forms of spectrum analyzers: •Swept tuned:is tuned by electronically sweeping its input over the desiredfrequency range thus, the frequency components of a signalare sampled sequentially in time.
Real time analyzers:They sample the total frequency range simultaneously, thuspreserving the time dependency between signals. Thistechnique allows both transient and periodic / random signals tobe displayed.
Basic Operation of Swept Tuned Spectrum AnalyzersSwept Tuned spectrum analyzers are based on a Super Heterodyne receiver principle.The input Frequency fin isconverted to an IntermediateFrequency, fIF , via a mixer(Multiplier) and a tunable local fIN = fLO + fIFoscillator fLO . When thefrequency difference betweenthe input signal and the localoscillator is equal to theintermediate frequency thenthere is a response on thedisplay.
Block Diagram of SWEPT Spectrum AnalyzerMultiple Frequency Translation via Multi-stageMixers and Multiple Local Oscillators (derived fromthe HARMONICS of the Local Oscillator)
Characteristics of Spectrum Analyzersa) Wide frequency range.b) Amplitude and frequency calibration via internal calibration source and error correction routines.c) Flat frequency response where amplitude is independent of frequency.d) Good frequency stability using synthesized local oscillators and reference source.e) Low internal distortion.f) Good frequency resolution.g) High amplitude sensitivity.h) Linear and logarithmic display modes for amplitude (voltage and dB scaling).i) Absolute and relative measurement capabilities.
Frequency RangeThe lower frequency limit of a spectrum analyzer is determined by the sideband noise of the local oscillator. The local oscillator feed through occurs even when there is no input signal present.The sensitivity at the lower frequency is also limited by the LOsideband noise.
COUPLINGAs the IF bandwidth is reduced, the time to sweep a given frequency range increases since the charge time of the IF filter increases.This means that the sweep time is increased to allow the IF filter to respond and therefore present an undistorted signal to the detector. These variables are generally taken into account automatically within a spectrum analyzer and are referred to as „COUPLING‟.
Zero Frequency Span mode Oscilloscope ModeIf the local oscillator is manually tuned, thespectrum analyzer becomes a fixed-tuned receiver whose frequency is determined by that of the local oscillator. In this mode the analyzer will display the time domain function since the frequency component is fixed even though the scan generator is still sweeping the display.
Frequency Resolutioncalled “resolution bandwidth” is:“The ability to separate and measure two signals in close proximity”.It is determined by 3 primary factors:a) the IF filter bandwidth.b) the shape of the IF filter.c) the sideboard noise of the IF filter.The IF bandwidth is normally specified by f at -3dBThe RESOLUTION as f↑ ↓, BUT !! Remember:The CHARGE time of the IF filter → INCREASE SWEEP time.
Example of Narrow IF FilterNarrow IF bandwidths are required to distinguish the sidebands of AM and FM signals.
Filter Skirt Inclination or the „SHAPE FACTOR‟When measuring close-in spurious components, the shape of the IF filter becomes important.The skirt inclination is:the ratio of the filter bandwidth at -60dB to that at -3dB
Scanning TOO FASTGaussian filters have SF 12:1Some spectrum analyzers utilize digital filters with shape factor as low as 3:1 because sometimes they are better in terms of frequency resolution, but they do have the drawback of sharply increasing the scan time.As the scan time decreases, the displayed amplitude decreases and the apparent bandwidth increases.Consequently, frequency resolution and amplitude uncertainty get worse, and some analyzers will warn you that you are now in an „UNCAL‟ (Uncalibrated) mode.
Sensitivity and Noise FigureThe sensitivity of a spectrum analyzer is: its ability to detect signals of low amplitudeThe maximum sensitivity of the analyzer is limited by the noise PN generated internally:Noise Increases with BANDWIDTH →
NOISE FIGURE FNIt is defined as :FN (S / N ) IN / (S / N )OUTWhere : S Signal, and N Noisein a dim ensionless quantity :F 10 log( FN ) dB
Video Filtering - AveragingVery low level signals can be difficult to distinguish from the internal noise; since analyzers display signal plus noise. some form of averaging or filtering is required to assist the visual detection process.So we use a post-detection video filter (Low Pass Filter) that (S N ) 2 N averages the internal noise of the analyzer. The minimum (S N ) / N 2 signal power that can be Minimum Signal level displayed = the average noise power 10log 2 3 dB
Signal Display Rangeis dependent on two key parameters:a) The minimum resolution bandwidth available and hence the average noise level.b) The maximum signal level at the first mixer that does not introduce distortion or inflict permanent damage to the mixer performance.
The Dynamic RangeIt is determined by 4 key factors:i. Average noise level: Which is generated within the RF section.ii. Residual spurious components:The harmonics of various signals are mixed together in a complex form and converted (via the MIXERS) to the IF signal components which are then displayed regardless of whether or not a signal is present at the input.iii. Distortion due to higher order harmonics:When the input signal level is high, spurious images of the input signal harmonics are generated due to the non-linearity of the mixer conversion!!!iv. Distortion due to 3rd order intermodulation products: • When two adjacent signals at high power are present as inputs to a spectrum analyzer, intermodulation occurs in the mixers, so Spurious signals, separated by the frequency difference of the input signals are generated above and below the input signals. The range over which measurements can be performed without interference from any of these factors is the dynamic range
AM MeasurementsFor an AM signal there are three signal elements:a) the unmodulated carrier.b) the upper sideboard whose frequency is the sum of the carrier and the modulation frequency.c) the lower sideboard whose frequency is the difference between the carrier and the modulation frequency.
In mobile radio communications, the emitted electromagnetic wavesoften do not reach the receiving antenna directly due to obstaclesblocking the line-of-sight path. In fact, the received waves are asuperposition of waves coming from all directions due to reflection,diffraction, and scattering caused by buildings, trees, and otherobstacles. This effect is known as multipath propagation.
Consequences of MultiPath Propagation !!The received signal consists an infinitesum of:1- attenuated2- delayed3- and phase-shifted replicas of the transmitted signal, each influencing each other.
Importance of Angle of Arrival f → f cos(α) !!!
Typical Received Signal
A Wireless Network
An Analog Transmission system
Characteristics of Analog TransmissionAnalog transmission is characterized by the following:1. Signal processing. Processing is performed on the baseband signal before modulation and after demodulation in order to improve the quality of the link.2. The number of communication channels supported by the carrier. In the case of a single communication channel, one refers to single channel per carrier (SCPC) transmission. Several communication channels combined by frequency division multiplexing (FDM) is referred to as FDM transmission.3. The type of modulation used. The most widely used is FM. For this type of modulation, the carrier amplitude is not affected by the modulating signal; thus, it is robust with respect to the nonlinearities of the channel.
Noise and Interference in Analog TransmissionThe signal received at the demodulator of a receiver isalways accompanied by noise, including that generated inpreceding stages of the receiver itself. Furthermore, theremay be interfering signals in the desired band that are notrejected by the bandpass filter HR(f ). Both noise andinterference give rise to undesired components at thedetector output. When interference or noise is included,the contaminated signal u(t ) is given by:
Simple Interference Example A sinusoidal carrier fc and an interference signal fILet the interference signal have amplitude Ai and frequencyfc + fi . The total signal entering the demodulator is thesum of two sinusoids, given by:
Following the phasor construction:
If the interference is small compared to the carrier, thephasor diagram shows that the resultant envelope isessentially the sum of the inphase components, while thequadrature component determines the phase angle. That is, ifAi << A, then:
we can see that the interfering wave performs anAM modulation and phase modulation of a carrierjust like a modulating tone of frequency f i withmodulation index mI