CHAPTER 4 RF/IF CIRCUITS - Analog Devices
RF/IF CIRCUITSCHAPTER 4 RF/IF CIRCUITSINTRODUCTIONSECTION 4.1: MIXERSTHE IDEAL MIXERDIODE-RING MIXERBASIC OPERATION OF THE ACTIVE MIXERREFERENCESSECTION 4.2: MODULATORSSECTION 4.3: ANALOG MULTIPLIERSREFERENCESSECTION 4.4: LOGARITHMIC AMPLIFIERSREFERENCESSECTION 4.5: TRUE-POWER DETECTORSSECTION 4.6: VARIABLE GAIN AMPLIFIERVOLTAGE CONTROLLED AMPLIFIERSX-AMPSDIGITALLY CONTROLLED VGAsREFERENCESSECTION 4.7: DIRECT DIGITAL SYNTHESISDDSALIASING IN DDS SYTEMSDDS SYSTEMS AS ADC CLOCK DRIVERSAMPLITUDE MODULATION IN A DDS SYSTEMSPURIOUS FREE DYNAMIC RANGE CONSIDERATIONSREFERENCESSECTION 4.8: PHASE-LOCKED LOOPSPLL SYNTHESIZER BASIC BUILDING BLOCKSTHE REFERENCE COUNTERTHE FEEDBACK COUNTER, NFRACTIONAL-N SYNTHESIZERSNOISE IN OSCILLATOR SYSTEMSPHASE NOISE IN VOLTAGE-CONTROLLED OSCILLATORSLEESON'S EQUATIONCLOSING THE LOOPPHASE NOISE MEASUREMENTSREFERENCE SPURSCHARGE PUMP LEAKAGE .514.534.564.564.594.604.614.624.644.674.694.70
BASIC LINEAR DESIGNSECTION 4.8: PHASE-LOCKED LOOPS (cont.)REFERENCES4.73
RF/IF CIRCUITSINTRODUCTIONCHAPTER 4: RF/IF CIRCUITSIntroductionFrom cellular phones to 2-way pagers to wireless Internet access, the world is becomingmore connected, even though wirelessly. No matter the technology, these devices arebasically simple radio transceivers (transmitters and receivers). In the vast majority ofcases the receivers and transmitters are a variation on the superheterodyne radio shown inFigure 4.1 for the receiver and Figure 4.2 for the transmitter.AGCRFDEMODIFLOLOFigure 4.1: Basic Superheterodyne Radio ReceiverRFMODIFLOLOFigure 4.2: Basic Superheterodyne Radio Transmitter4.1
BASIC LINEAR DESIGNThe basic concept of operation is as follows. For the receiver, the signal from the antennais amplified in the radio frequency (RF) stage. The output of the RF stage is one input ofa mixer. A Local Oscillator (LO) is the other input. The output of the mixer is at theIntermediate Frequency (IF). The concept here is that is much easier to build a high gainamplifier string at a narrow frequency band than it is to build a wideband, high gainamplifier. Also, the modulation bandwidth is typically very much smaller than the carrierfrequency. A second mixer stage converts the signal to the baseband. The signal is thendemodulated (demod). The modulation technique is independent from the receivertechnology. The modulation scheme could be amplitude modulation (AM), frequencymodulation (FM), phase modulation or some form of quadrature amplitude modulation(QAM), which is a combination of amplitude and phase modulation.To put some numbers around it, let us consider a broadcast FM signal. The carrierfrequency is in the range of 98 MHz to 108 MHz. The IF frequency is almost always10.7 MHz. The baseband is 0 Hz to 15 kHz. This is the sum of the right and left audiofrequencies. There is also a modulation band centered at 38 kHz that is the difference ofthe left and right audio signals. This difference signal is demodulated and summed withthe sum signal to generate the separate left and right audio signals.On the transmit side the mixers convert the frequencies up instead of down.These simplified block diagrams neglect some of the refinements that may beincorporated into these designs, such as power monitoring and control of the transmitterpower amplifier as achieved with the “True-Power” circuits.As technology has improved, we have seen the proliferation of IF sampling. ADCs ofsufficient performance have been developed which allows the sampling of the signal atthe IF frequency range, with demodulation occurring in the digital domain. This allowsfor system simplification by eliminating a mixer stage.In addition to the basic building blocks that are the subject of this chapter, these circuitblocks often appear as building blocks in larger application specific integrated circuits(ASIC).4.2
RF/IF CIRCUITSMIXERSECTION 4.1: MIXERSThe Ideal MixerAn idealized mixer is shown in Figure 4.3. An RF (or IF) mixer (not to be confused withvideo and audio mixers) is an active or passive device that converts a signal from onefrequency to another. It can either modulate or demodulate a signal. It has three signalconnections, which are called ports in the language of radio engineers. These three portsare the radio frequency (RF) input, the local oscillator (LO) input, and the intermediatefrequency (IF) output.IDEAL MIXERIF OUTPUTRF INPUTfRFfRF fLOfRF - fLOLO INPUTfLOFigure 4.3: The Mixing ProcessA mixer takes an RF input signal at a frequency fRF, mixes it with a LO signal at afrequency fLO, and produces an IF output signal that consists of the sum and differencefrequencies, fRF fLO. The user provides a bandpass filter that follows the mixer andselects the sum (fRF fLO) or difference (fRF – fLO) frequency.Some points to note about mixers and their terminology: When the sum frequency is used as the IF, the mixer is called an upconverter; when thedifference is used, the mixer is called a downconverter. The former is typically used in atransmit channel, the latter in a receive channel. In a receiver, when the LO frequency is below the RF, it is called low-side injection andthe mixer a low-side downconverter; when the LO is above the RF, it is called high-sideinjection, and the mixer a high-side downconverter.4.3
BASIC LINEAR DESIGN Each of the outputs is only half the amplitude (one-quarter the power) of the individualinputs; thus, there is a loss of 6 dB in this ideal linear mixer. (In a practical multiplier, theconversion loss may be greater than 6 dB, depending on the scaling parameters of thedevice. Here, we assume a mathematical multiplier, having no dimensional attributes.)A mixer can be implemented in several ways, using active or passive techniques.Ideally, to meet the low noise, high linearity objectives of a mixer we need some circuitthat implements a polarity-switching function in response to the LO input. Thus, themixer can be reduced to Figure 4.4, which shows the RF signal being split into in-phase(0 ) and anti-phase (180 ) components; a changeover switch, driven by the localoscillator (LO) signal, alternately selects the in-phase and antiphase signals. Thusreduced to essentials, the ideal mixer can be modeled as a sign-switcher. 1RF INPUTIF OUTPUT-1SWITCH, fLOFigure 4.4: An Ideal Switching MixerIn a perfect embodiment, this mixer would have no noise (the switch would have zeroresistance), no limit to the maximum signal amplitude, and would develop nointermodulation between the various RF signals. Although simple in concept, thewaveform at the intermediate frequency (IF) output can be very complex for even a smallnumber of signals in the input spectrum. Figure 3.43 shows the result of mixing just asingle input at 11 MHz with an LO of 10 MHz.The wanted IF at the difference frequency of 1 MHz is still visible in this waveform, andthe 21 MHz sum is also apparent. How are we to analyze this?We still have a product, but now it is that of a sinusoid (the RF input) at ωRF and avariable that can only have the values 1 or –1, that is, a unit square wave at ωLO. Thelatter can be expressed as a Fourier seriesSLO 4/π { sinωLOt - 1/3 sin3ωLOt 1/5 sin5ωLOt – . . . . }4.4Eq. 4-1
RF/IF CIRCUITSMIXERFigure 4.5: Inputs and Output for an Ideal Switching Mixerfor fRF 11MHz, fLO 10MHzThus, the output of the switching mixer is its RF input, which we can simplify as sinωRFt,multiplied by the above expansion for the square wave, producingSIF 4/π { sinωRFt sinωLOt – 1/3 sinωRFt sin3ωLOt 1/5 sin5ωRFt sin5ωLOt – . . . . }Eq. 4-2Now expanding each of the products, we obtainSIF 2/π { sin(ωRF ωLO)t sin(ωRF – ωLO)t– 1/3 sin(ωRF 3ωLO)t – 1/3 sin(ωRF – 3ωLO)t 1/5 sin(ωRF 5ωLO)t 1/5 sin(ωRF – 5 ωLO)t – . . . }Eq. 4-3or simplySIF 2/π{ sin(ωRF ωLO)t sin(ωRF – ωLO)t harmonics }Eq. 4-4The most important of these harmonic components are sketched in Figure 4.6 for theparticular case used to generate the waveform shown in Figure 4.5, that is, fRF 11 MHzand fLO 10 MHz. Because of the 2/π term, a mixer has a minimum 3.92 dB insertionloss (and noise figure) in the absence of any gain.4.5
BASIC LINEAR DESIGN0.8LINEARAMPLITUDE0.637 -3.9dB0.212 -13.5dB0.127 -17.9dB0.090 -20.9dB0.6370.6370.6WANTED IFAT 1MHzSUM 0FREQUENCY (MHz)Figure 4.6: Output Spectrum for a Switching Mixerfor fRF 11MHz and fLO 10MHzNote that the ideal (switching) mixer has exactly the same problem of image response toωLO – ωRF as the linear multiplying mixer. The image response is somewhat subtle, as itdoes not immediately show up in the output spectrum: it is a latent response, awaiting theoccurrence of the “wrong” frequency in the input spectrum.Diode-Ring MixerFor many years, the most common mixer topology for high-performance applications hasbeen the diode-ring mixer, one form of which is shown in Figure 4.7. The diodes, whichmay be silicon junction, silicon Schottky-barrier or gallium-arsenide types, provide theessential switching action. We do not need to analyze this circuit in great detail, but notein passing that the LO drive needs to be quite high—often a substantial fraction of onewatt—in order to ensure that the diode conduction is strong enough to achieve low noiseand to allow large signals to be converted without excessive spurious nonlinearity.Because of the highly nonlinear nature of the diodes, the impedances at the three ports arepoorly controlled, making matching difficult. Furthermore, there is considerable couplingbetween the three ports; this, and the high power needed at the LO port, make it verylikely that there will be some component of the (highly-distorted) LO signal coupled backtoward the antenna. Finally, it will be apparent that a passive mixer such as this cannotprovide conversion gain; in the idealized scenario, there will be a conversion loss of 2/π[as Eq. 4-4 shows], or 3.92 dB. A practical mixer will have higher losses, due to theresistances of the diodes and the losses in the transformers.4.6
RF/IF CIRCUITSMIXERRFINLOINIFOUTFigure 4.7: Diode-Ring MixerUsers of this type of mixer are accustomed to judging the signal handling capabilities bya Level rating. Thus, a Level-17 mixer needs 17 dBm (50 mW) of LO drive and canhandle an RF input as high as 10 dBm ( 1 V). A typical mixer in this class would be theMini-Circuits LRMS-1H, covering 2 MHz to 500 MHz, having a nominal insertion lossof 6.25 dB (8.5 dB max), a worst-case LO-RF isolation of 20 dB and a worst-case LO-IFisolation of 22 dB (these figures for an LO frequency of 250 MHz to 500 MHz). Theprice of this component is approximately 10.00 in small quantities. Even the mostexpensive diode-ring mixers have similar drive power requirements, high losses and highcoupling from the LO port.The diode-ring mixer not only has certain performance limitations, but it is also notamenable to fabrication using integrated circuit technologies, at least in the form shownin Figure 4.7. In the mid sixties it was realized that the four diodes could be replaced byfour transistors to perform essentially the same switching function. This formed the basisof the now-classical bipolar circuit shown in Figure 4.8, which is a minimal configurationfor the fully-balanced version. Millions of such mixers have been made, includingvariants in CMOS and GaAs. We will limit our discussion to the BJT form, an exampleof which is the Motorola MC1496, which, although quite rudimentary in structure, hasbeen a mainstay in semi-discrete receiver designs for about 25 years.The active mixer is attractive for the following reasons: It can be monolithically integrated with other signal processing circuitry. It can provide conversion gain, whereas a diode-ring mixer always has an insertion loss.(Note: Active mixers may have gain. The Analog Devices' AD831 active mixer, forexample, amplifies the result in Eq. 4-4 by π/2 to provide unity gain from RF to IF.) It requires much less power to drive the LO port. It provides excellent isolation between the signal ports.4.7
BASIC LINEAR DESIGN Is far less sensitive to load-matching, requiring neither diplexer nor broadbandtermination.Using appropriate design techniques it can provide trade-offs between third-orderintercept (3OI or IP3) and the 1 dB gain-compression point (P1dB), on the one hand, andtotal power consumption (PD) on the other. (That is, including the LO power, which in apassive mixer is hidden in the drive circuitry.)Basic Operation of the Active MixerUnlike the diode-ring mixer, which performs the polarity-reversing switching function inthe voltage domain, the active mixer performs the switching function in the currentdomain. Thus the active mixer core (transistors Q3 through Q6 in Figure 4.8) must bedriven by current-mode signals. The voltage-to-current converter formed by Q1 and Q2receives the voltage-mode RF signal at their base terminals and transforms it into adifferential pair of currents at their collectors.IF OUTPUTQ3Q4Q6Q5LOINPUTQ1Q2RFINPUTIEEFigure 4.8: Classic Active MixerA second point of difference between the active mixer and diode ring mixer, therefore, isthat the active mixer responds only to magnitude of the input voltage, not to the inputpower; that is, the active mixer is not matched to the source. (The concept of matching isthat both the current and the voltage at some port are used by the circuitry which formsthat port). By altering the bias current, IEE, the transconductance of the input pair Q1–Q24.8
RF/IF CIRCUITSMIXERcan be set over a wide range. Using this capability, an active mixer can provide variablegain.A third point of difference is that the output (at the collectors of Q3–Q6) is in the form ofa current, and can be converted back to a voltage at some other impedance level to thatused at the input, hence, can provide further gain. By combining both output currents(typically, using a transformer) this voltage gain can be doubled. Finally, it will beapparent that the isolation between the various ports, in particular, from the LO port tothe RF port, is inherently much lower than can be achieved in the diode ring mixer, dueto the reversed-biased junctions that exist between the ports.Briefly stated, though, the operation is as follows. In the absence of any voltagedifference between the bases of Q1 and Q2, the collector currents of these two transistorsare essentially equal. Thus, a voltage applied to the LO input results in no change ofoutput current. Should a small dc offset voltage be present at the RF input (due typicallyto mismatch in the emitter areas of Q1 and Q2), this will only result in a smallfeedthrough of the LO signal to the IF output, which will be blocked by the first IF filter.Conversely, if an RF signal is applied to the RF port, but no voltage difference is appliedto the LO input, the output currents will again be balanced. A small offset voltage (duenow to emitter mismatches in Q3–Q6) may cause some RF signal feedthrough to the IFoutput; as before, this will be rejected by the IF filters. It is only when a signal is appliedto both the RF and LO ports that a signal appears at the output; hence, the term doublybalanced mixer.Active mixers can realize their gain in one other way: The matching networks used totransform a 50 Ω source to the (usually) high input impedance of the mixer provides animpedance transformation and thus voltage gain due to the impedance step up. Thus, anactive mixer that has loss when the input is terminated in a broadband 50 Ω terminationcan have “gain” when an input matching network is used.4.9
BASIC LINEAR DESIGNREFERENCES:1.Barrie Gilbert, ISSCC Digest of Technical Papers 1968, pp. 114-115, February 16, 1968.2.Barrie Gilbert, Journal of Solid State Circuits, Vol. SC-3, December 1968, pp. 353-372.3.C.L. Ruthroff, Some Broadband Transformers, Proc. I.R.E., Vol.47, August, 1959,pp.1337-1342.4.James M. Bryant, Mixers for High Performance Radio, Wescon 1981: Session 24 (Published byElectronic Conventions, Inc., Sepulveda Blvd., El Segundo, CA)5.P.E. Chadwick, High Performance IC Mixers, IERE Conference on Radio Receivers andAssociated Systems, Leeds, 1981, IERE Conference Publication No. 50.6.P.E. Chadwick, Phase Noise, Intermodulation, and Dynamic Range, RF Expo, Anaheim, CA,January, 1986.7.AD831 Data Sheet, Rev. B, Analog Devices.4.10
RF/IF CIRCUITSMODULATORSECTION 4.2: MODULATORSModulators (sometimes called balanced-modulators, doubly-balanced modulators oreven on occasions high level mixers) can be viewed as sign-changers. The two inputs, Xand Y, generate an output W, which is simply one of these inputs (say, Y) multiplied byjust the sign of the other (say, X), that is W Y* sign (X). Therefore, no referencevoltage is required. A good modulator exhibits very high linearity in its signal path, withprecisely equal gain for positive and negative values of Y, and precisely equal gain forpositive and negative values of X. Ideally, the amplitude of the X input needed to fullyswitch the output sign is very small, that is, the X-input exhibits a comparator-likebehavior. In some cases, where this input may be a logic signal, a simpler X-channel canbe used.As an example, the AD8345 is a silicon RFIC quadrature modulator, designed for usefrom 250 MHz to 1000 MHz. Its excellent phase accuracy and amplitude balance enablethe high performance direct modulation of an IF carrier.The AD8345 accurately splits the external LO signal into two quadrature componentsthrough the polyphase phase-splitter network. The two I and Q LO components are mixedwith the baseband I and Q differential input signals. Finally, the outputs of the twomixers are combined in the output stage to provide a single-ended 50 Ω drive at VOUT.Figure 4.9: AD8345 Block Diagram4.11
BASIC LINEAR DESIGNNotes:4.12
RF/IF CIRCUITSANALOG MULTIPLIERSSECTION 4.3: ANALOG MULTIPLIERSA multiplier is a device having two input ports and an output port. The signal at theoutput is the product of the two input signals. If both input and output signals arevoltages, the transfer characteristic is the product of the two voltages divided by a scalingfactor, K, which has the dimension of voltage (see Figure 4.10). From a mathematicalpoint of view, multiplication is a four quadrant operation—that is to say that both inputsmay be either positive or negative and the output can be positive or negative. Some of thecircuits used to produce electronic multipliers, however, are limited to signals of onepolarity. If both signals must be unipolar, we have a single quadrant multiplier, and theoutput will also be unipolar. If one of the signals is unipolar, but the other may haveeither polarity, the multiplier is a two quadrant multiplier, and the output may have eitherpolarity (and is bipolar). The circuitry used to produce one- and two-quadrant multipliersmay be simpler than that required for four quadrant multipliers, and since there are manyapplications where full four quadrant multiplication is not required, it is common to findaccurate devices which work only in one or two quadrants. An example is the AD539, awideband dual two-quadrant multiplier which has a single unipolar Vy input with arelatively limited bandwidth of 5 MHz, and two bipolar Vx inputs, one per multiplier,with bandwidths of 60 MHz. A block diagram of the AD539 is shown in Figure 4.12.VxV out VxVyVyKK SCALE FACTORFigure 4.10: An Analog Multiplier Block DiagramTypeVXVYVoutSingle QuadrantUnipolarUnipolarUnipolarTwo QuadrantBipolarUnipolarBipolarFour QuadrantBipolarBipolarBipolarFigure 4.11: Definition of Multiplier Quadrants4.13
BASIC LINEAR DESIGNZ1W1VX1VW1 CH1MULTCH2MULT-VX1 VYEXTERNALOP AMPSVYVW2 VX2-VX2 VYW2Z2Figure 4.12: AD539 Block DiagramThe simplest electronic multipliers use logarithmic amplifiers. The computation relies onthe fact that the antilog of the sum of the logs of two
RF/IF CIRCUITS MIXER 4.5 Figure 4.5: Inputs and Output for an Ideal Switching Mixer for f RF 11MHz, f LO 10MHz Thus, the output of the switching mixer is its RF input, which we can simplify as sinωRFt, multiplied by the above expansion for the square wave, producing
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
Contemporary Electric Circuits, 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 1 Strangeway, Petersen, Gassert, and Lokken CHAPTER 9 Series–Parallel Analysis of AC Circuits Chapter Outline 9.1 AC Series Circuits 9.2 AC Parallel Circuits 9.3 AC Series–Parallel Circuits 9.4 Analysis of Multiple-Source AC Circuits Using Superposition 9.1 AC SERIES CIRCUITS
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
circuits, all the current flows through one path. In parallel circuits, current can flow through two or more paths. Investigations for Chapter 9 In this Investigation, you will compare how two kinds of circuits work by building and observing series and parallel circuits. You will explore an application of these circuits by wiring two switches .
About the husband’s secret. Dedication Epigraph Pandora Monday Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Tuesday Chapter Six Chapter Seven. Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Chapter Fifteen Chapter Sixteen Chapter Seventeen Chapter Eighteen
18.4 35 18.5 35 I Solutions to Applying the Concepts Questions II Answers to End-of-chapter Conceptual Questions Chapter 1 37 Chapter 2 38 Chapter 3 39 Chapter 4 40 Chapter 5 43 Chapter 6 45 Chapter 7 46 Chapter 8 47 Chapter 9 50 Chapter 10 52 Chapter 11 55 Chapter 12 56 Chapter 13 57 Chapter 14 61 Chapter 15 62 Chapter 16 63 Chapter 17 65 .
HUNTER. Special thanks to Kate Cary. Contents Cover Title Page Prologue Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter
