Chapter 4 Bandpass Circuits Limiters Mixers, Upconverters and Downconverters

1. Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University • Chapter 4 • Bandpass Circuits • Limiters • Mixers, Upconverters and Downconverters • Detectors, Envelope Detector, Product Detector • Phase Locked Loops (PLL)

2. Limiters • Limiter is a nonlinear circuit with an output saturation characteristic. • It rejects envelope variations but preserves the phase variations.

3. 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 Input signal: Output:

4. Mixers (Choosing LO Freq.) Up-conversion Down-conversion Bandpass Filter Baseband/bandpass Filter (fc-f0) • If (fc- f0)= 0  Low Pass Filter gives baseband spectrum • If (fc- f0 )> 0  Bandpass filter  Modulation is preserved Filter Output: • If fc>f0  modulation on the mixer input is preserved ‘’ needs to be positive • If fc<f0 Complex envelope is conjugated ~sidebands are exchanged -f→Upper & lower sidebands are exchanged * → Phase spectrum is inverted

5. - Amplitude is scaled by A0/2 i.e., f0>fc down conversion with high-side injection - Amplitude is scaled by A0/2 - Sidebands are reversed from those on the input Mixers (Up Converter and Down Converter) • Complex envelope of an Up Converter: • Complex envelope of a Down Converter: i.e., f0<fc down conversion with low-side injection - Amplitude is scaled by A0/2

6. Mixer Realizations Without Multipliers Multiplication operation needed by mixers can be obtained by using a nonlinear device together with a summer. Multiplication operation needed by mixers can also be obtained by using an analog switch.

7. 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.

8. Detector Circuits Signal processing Carrier circuits Transmission medium (Channel) Carrier circuits Signal processing Information input m • 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 Detector Circuits

9. Envelope Detector Envelope Detector Output: Bandpass input: K – Proportionality Constant • Ideal envelope detector: Waveform at the output is a real envelope R(t) of its input Diode Envelope Detector Circuit

10. Envelope Detector • The Time Constant RC must be chosen so that the envelope variations can be followed. • In AM, detected DC is used for Automatic Gain Control (AGC)

11. 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: LPF passes down conversion component: Where g(t) is the complex envelope of the input and x(t) & y(t) are the quadrature components of the input:

12. Different Detectors Obtained from Product Detector The product detector output is or If the phase difference is small • Oscillator phase synchronized with the in-phase component • We obtain INPHASE DETECTOR. • We obtain QUADRATURE PHASE DETECTOR • We obtain ENVELOPE DETECTOR If the input has no angle modulation and reference phase (θ0) =0 • We obtain PHASE DETECTOR If an angle modulated signal is present at the input and reference phase (θ0) =90 The output is proportional to the Phase difference (Sinusoidal phase characteristics)

13. Frequency Modulation Detector • A ideal FM Detector is a device that produces an output that is proportional to the instantenous frequency of the input. • The DC output can easily be blocked

14. Frequency Detector Using Freq. to Amplitude Conversion

15. 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

16. 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.

17. Phase Locked Loop (PLL) Let input signal be : Let the VCO output be: The phase detector output v1(t) is given by : The sum frequency term is rejected by LPF so the filter output v2(t) is: • 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/capturerange

18. Phase Locked Loop (PLL) • Various types of Phase Detector characteristics used in PLL’s.

19. 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

20. 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.