* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Exponential Carrier Wave Modulation
Switched-mode power supply wikipedia , lookup
405-line television system wikipedia , lookup
Cellular repeater wikipedia , lookup
Schmitt trigger wikipedia , lookup
Telecommunication wikipedia , lookup
Signal Corps (United States Army) wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Radio direction finder wikipedia , lookup
Operational amplifier wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Power electronics wikipedia , lookup
Audio crossover wikipedia , lookup
Integrating ADC wikipedia , lookup
Direction finding wikipedia , lookup
Superheterodyne receiver wikipedia , lookup
Analog-to-digital converter wikipedia , lookup
Signal Corps Laboratories wikipedia , lookup
Oscilloscope history wikipedia , lookup
Analog television wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Regenerative circuit wikipedia , lookup
Interferometric synthetic-aperture radar wikipedia , lookup
Opto-isolator wikipedia , lookup
Rectiverter wikipedia , lookup
High-frequency direction finding wikipedia , lookup
Index of electronics articles wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
S-72.245 Transmission Methods in Telecommunication Systems (4 cr) Carrier Wave Modulation Systems Phase-locked loops (PLLs) 2 Phase-locked loop is a feedback arrangement capable to synchronize itself to a noisy external reference The output signals of the loop can be used to produce for instance multitude of locked frequencies PLL application areas include... – modulators – demodulators – frequency synthesis – multiplexers – signal processors Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen The PLL principle The PLL circuit consists of – phase comparator (in the figure below the multiplier) – lowpass filter – feedback amplifier – VCO (voltage controlled oscillator), whose output frequency is linearly proportional to input amplitude Principle: phase difference of Xc(t) and v(t) adjusts VCO Phase comparator output is comparable to phase difference of input signals 3 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen PLL phase comparator realizations Circuits: (a) analog and (b) digital phase comparator circuit Note that for (a) output is proportional to – input signal phase difference – input signal amplitudes (unintended AM thus harmful) In (b) AM effects are compensated and response is more linear pulse ratio: 50/50 ideal XOR-circuit 4 sin(a cos( ) 1 sin( ) 1 sin( ) 2 2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen FM detection by PLL time domain sin (t ) (t ) (t ) v (t ) (t ) 2 K y(t )dt phase domain v t v dv (t ) (t ) dt t v (t ) ( ) d 5 frequency domain t v ( ) d Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen 1 V ( f ) 1 V (0) ( f ) 2 j 2 f PLL FM-demodulator: the feedback analysis Solve transfer function with feedback: Y( f ) Y ( f ) X ( f ) H 2 ( f )Y ( f ) H1 ( f ) Y ( f ) H1 ( f ) H 2 ( f )Y ( f ) X ( f ) H1 ( f ) Y( f ) H1 ( f ) X(f ) 1 H1 ( f ) H 2 ( f ) This is applied to the linearized PLL yielding relationship between the input phase and output voltage: Ka H ( f ) Y( f ) ( f ) 1 K a H ( f ) K v / jf 1 jfKH ( f ) ( f ) K v jf KH ( f ) (K Ka Kv ) 6 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Applying the FM signal to the linearized PLL model Remember the FM wave: d (t ) / dt 2 f x(t ) where the modulating signal is denoted by x(t). The input FM phase to the system is thus (t ) 2 f x( )d t This is in frequency domain: ( f ) 2 f X ( f ) /( j f ) assuming no DC component or V(0) = 0, or v ( ) d t 1 V ( f ) 1 V (0) ( f ) 2 j 2 f 0 7 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Applying FM signal to the detector... (cont.) Thus the input is ( f ) f X ( f ) /( jf ) and the output is 1 jfKH ( f ) f X ( f ) Y( f ) ( f ) HL ( f ) K v jf KH ( f ) Kv where the loop equivalent transfer function is Y(f) HL ( f ) H( f ) H ( f ) j( f / K ) K Ka Kv Assume that the first order LP function is used or f f X(f ) W 1 Y( f ) X ( f ), 1 Kv 1 j( f / K ) Kv K 1 j( f / K ) f y (t ) x(t ) Kv Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen HL ( f ) 8 PLL based frequency synthesizer Reference signal fin is locked for instance to the fundamental frequency of a crystal oscillator f in Phase detector Divide by 10 By adjusting the divider different frequencies can be produced whose phase is locked into fin 9 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen Filt. VCO f out 10 fin Detecting DSB using PLL-principle An important application for PLLs is in synchronization of receiver local oscillator in synchronous detection In the Costas PLL (below) two phase discriminators are used to: – cancel out DSB modulation x(t) in the driving signal – synchronize the output frequency to the center frequency of the DSB spectra (the suppressed carrier) – to detect the DSB signal Costas PLL detector for DSB PD: phase detector (=multiply+LPF) Loop drives phase error to zero 10 LPF yields constant (zero) output when loop is locked to carrier sin ss cos ss 1 sin 2 ss sin 0 ss 2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen