Chapter 4 Bandpass Circuits Limiters Mixers, Upconverters and Downconverters Detectors, Envelope Detector, Product Detector Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

Limiters Limiter is a nonlinear circuit with an output saturation characteristic. It rejects envelope variations but preserves the phase variations. Ideal limiter characteristic with illustrative input and unfiltered output waveforms.

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

Mixers

Choosing LO Frequency of Mixers 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

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

In practice the multiplying operation needed for the mixer is realized by on of the following: A continuously variable transconductance device, i.e. Dual-gate FET A non-linear device A linear device with a time-varying discrete-gain. Here we will look at 2nd approach.

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.

The output of the linear device is:  

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.

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

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

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)

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:

Different Detectors Obtained from Product Detector 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 product detector output is or If the phase difference is small The output is proportional to the Phase difference (Sinusoidal phase characteristics)

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. The DC output can easily be blocked

Frequency Detector Using Freq. to Amplitude Conversion Figure 4–16 Slope detection using a single-tuned circuit for frequency-to amplitude conversion.

Balanced Discriminator

Balanced zero-crossing FM detector.

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.

PLL, 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.

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/capture range

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

Figure 4–24 PLL used for coherent detection of AM. 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.

Figure 4–25 PLL used in a frequency synthesizer. 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. Figure 4–25 PLL used in a frequency synthesizer.