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Chapter 4 Bandpass Circuits Limiters Mixers, Upconverters and Downconverters Detectors, Envelope Detector, Product Detector Phase Locked Loops (PLL) Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng 360 1 Limiters Limiter is a nonlinear circuit with an output saturation characteristic. It rejects envelope variations but preserves the phase variations. vin(t ) R(t ) cos(ct (t )) vout (t ) KVL cos(ct (t )) Ideal limiter characteristic with illustrative input and unfiltered output waveforms. Eeng 360 2 Mixers Ideal mixer is a mathematical multiplier of two input signals. One of the signals is sinusoidal generated by a local oscillator. Mixing results in frequency translation. SSB mixer Bandpass Input Signal vin t Re gin t e jct Eeng 360 3 Mixers Bandpass Input Signal vin t Re gin t e jct Mixer Output v1 t A0 Re g in t e jct cos 0t A0 gin t e jct gin* t e jct e jct e jct 4 A j t j t j t j t 0 gin t e c 0 gin* t e c 0 gin t e c 0 gin* t e c 0 4 1 1 * Re 2 2 A A j t j t v1 t 0 Re g in t e c 0 0 Re g in t e c 0 2 2 fu f c f 0 fd fc f0 UPCONVERSION BANDPASS FILTER DOWNCONVERSION BASEBAND OR BANDPASS Eeng FILTE 360 R 4 Choosing LO Frequency of Mixers v1 t A0 A j t j t Re gin t e c 0 0 Re gin t e c 0 2 2 Up-conversion Down-conversion f d fc f0 fu fc f0 Baseband/bandpass Filter (fc-f0) Bandpass Filter If (fc- f0) = 0 Low Pass Filter gives baseband spectrum If (fc- f0 )> 0 Bandpass filter Modulation is preserved Filter Output: v2 t Reg 2 t e j c 0 t A2 Reg t e j c 0 t 0 in If fc>f0 modulation on the mixer input is preserved If fc<f0 A A v1 t 0 Re g in t e j c 0 t 0 Re g in* t e j 0 c t 2 2 ‘’ needs to be positive Complex envelope is conjugated ~ sidebands are exchanged * dt gin t e dt Gin* f - f Upper & lower sidebands are exchanged F g * in t g t e * in jt * Phase spectrum is inverted j t Eeng 360 5 Mixers (Up Converter and Down Converter) Complex envelope of an Up Converter: g 2 t A0 g in t ; 2 fu fc f0 0 - Amplitude is scaled by A0/2 Complex envelope of a Down Converter: f d f c f 0 0 i.e., f0<fc down conversion with low-side injection g 2 t A0 g in t 2 - Amplitude is scaled by A0/2 f d f 0 f c 0 i.e., f0>fc down conversion with high-side injection g2 A0 * g in t 2 - Amplitude is scaled by A0/2 - Sidebands are reversed from those on the input Eeng 360 6 Mixer Realizations Without Multipliers Multiplication operation needed by mixers can be obtained by using a nonlinear device together with a summer. Nonlinear device used as a mixer. Eeng 360 7 Mixer Realizations Without Multipliers Multiplication operation needed by mixers can also be obtained by using an analog switch. Linear time-varying device used as a mixer. Eeng 360 8 Mixer Realizations Without Multipliers Analysis of a double-balanced mixer circuit. Eeng 360 9 Frequency Multiplier Frequency Multipliers consists of a nonlinear device together with a tuned circuit. The frequency of the output is n times the frequency of the input. vin(t ) R(t ) cos(ct (t )) v1 (t ) K n v n in(t ) K n R n (t ) cos n (ct (t )) v1 (t ) CR n (t ) cos(nct n (t )) Other Terms vo (t ) CR n (t ) cos(nct n (t )) Eeng 360 10 Detector Circuits Detectors convert input bandpass waveform into an output baseband waveform. Detector circuits can be designed to produce R(t), Θ(t), x(t) or y(t). • Envelope Detector • Product Detector • Frequency Modulation Detector Information Signal g (t ) input processing m Carrier circuits s (t ) Transmission medium (Channel) r (t ) Carrier circuits g~ (t ) Signal processing ~ m Detector Circuits Eeng 360 11 Envelope Detector Ideal envelope detector: Waveform at the output is a real envelope R(t) of its input Bandpass input: vin (t ) Rt cosct t Envelope Detector Output: vout t KR t Rt 0 K – Proportionality Constant Diode Envelope Detector Circuit Eeng 360 12 Envelope Detector The Time Constant RC must be chosen so that the envelope variations can be followed. B 1 f c 2 RC In AM, detected DC is used for Automatic Gain Control (AGC) vout (t ) KR (t ) K g (t ) KAc 1 m(t ) DC Message Eeng 360 13 Product Detector Product Detector is a Mixer circuit that down converts input to baseband. fc- Freq. of the oscillator θ0- Phase of the oscillator Output of the multiplier: v1 t R t cos ct t A0 cos ct 0 1 1 A0 R t cos t 0 A0 R t cos 2ct t 0 2 2 LPF passes down conversion component: 1 1 A0 R t cos t 0 A0 Re g t e j0 g (t ) R (t )e j (t ) x (t ) jy (t ) 2 2 Where g(t) is the complex envelope of the input and x(t) & y(t) are the quadrature components of the input: vout t Eeng 360 14 Different Detectors Obtained from Product Detector Oscillator phase synchronized with the in-phase component vout t if 0 0 : 1 A0 xt 2 We obtain INPHASE DETECTOR. We obtain QUADRATURE PHASE DETECTOR if 0 90 We obtain ENVELOPE DETECTOR If the input has no angle modulation and reference phase (θ0) =0 We obtain PHASE DETECTOR If an angle if modulated signal is present at the input and reference phase (θ0) =90 The product detector output is If the phase difference is small vout t 1 A0 Ac t 2 if t 0 1 A0 y t 2 vout 1 A0 Rt 2 0 90 vin (t ) A cos ct t 1 A0 Re Ac e j t 90 2 vout t vout c or vout t 1 A0 Ac sin t 2 sin t t The output is proportional to the Phase difference (Sinusoidal phase characteristics) Eeng 360 15 Frequency Modulation Detector A ideal FM Detector is a device that produces an output that is proportional to the instantenous frequency of the input. Frequency demodulation using slope detection. vin (t ) A(t ) cos[ct (t )] t (t ) K f m( )d d (t ) v1 (t ) VL cos[ct (t )] v2 (t ) VL c sin[ct (t )] dt d (t ) d (t ) vout (t ) VL c V L c dt dt VLc VL K f m(t ) DC AC (Proportional to m(t )) • The DC output can easily be blocked Eeng 360 16 Frequency Detector Using Freq. to Amplitude Conversion Figure 4–16 Slope detection using a single-tuned circuit for frequency-to amplitude conversion. Eeng 360 17 Balanced Discriminator Eeng 360 18 Balanced zero-crossing FM detector. Eeng 360 19 Phase Locked Loop (PLL) PLL can be used to Track Phase and Frequency of the carrier component of the incoming signal Three basic components: - Phase Detector : Multiplier (phase comparator) - VCO : Voltage Controlled Oscillator - Loop filter: LPF Operation is similar to a feedback system Basic PLL. Eeng 360 20 PLL, Voltage Controlled Oscillator (VCO) Voltage Controlled Oscillator (VCO): Oscillator frequency is controlled by external voltage Oscillation frequency varies linearly with input voltage If e0(t) – VCO input voltage, then its output is a sinusoid of frequency (t)=c+ce0(t) c - free-running frequency of the VCO. The multiplier output is further low-pass-filtered & then input to VCO This voltage changes the frequency of the oscillator & keeps it locked. Eeng 360 21 Phase Locked Loop (PLL) Let input signal be : vin (t ) Ai sin[ ct i (t )] t o (t ) K v v2 ( )d Let the VCO output be: vo (t ) Ao cos[ct o (t )] The phase detector output v1(t) is given by : v1 (t ) K m Ai Ao sin[ ct i (t )] cos[ ct 0 (t )] K m Ai Ao sin[ i (t ) - 0 (t)] sin[2 ct i (t ) 0 (t)] 2 The sum frequency term is rejected by LPF so the filter output v2(t) is: v2 (t ) K d [sin e (t)] f (t ) where e (t) i (t) - o (t) and Kd K m Ai Ao 2 e(t) is called the Phase Error. The Phase Error voltage characteristics is SINUSOIDAL. A PLL can track the incoming frequency only over a finite range Lock/hold-in range The frequency range over which the input will cause the loop to lock pull-in/capture range Eeng 360 22 Phase Locked Loop (PLL) Various types of Phase Detector characteristics used in PLL’s. Eeng 360 23 Aplications of PLL PLL used for coherent detection of AM signals. • A synchronized carrier signal is generated by the PLL. • VCO locks with 90 phase difference so a -90 extra phase shift is needed. • The generated carrier is used with a product detector to recover the envelope Figure 4–24 PLL used for coherent detection of AM. Eeng 360 24 Aplications of PLL PLL used as a frequency synthesizer. Frequency dividers use integer values of M and N. For M=1 frequency synthesizer acts as a frequency multiplier. f x f out M N f out N fx M Figure 4–25 PLL used in a frequency synthesizer. Eeng 360 25