DESIGN AND IMPLEMENTATION OF ANALOG MULTIPLIERS AND IC’s

1. DESIGN AND IMPLEMENTATION OF ANALOG MULTIPLIERS AND IC’s

2. Introduction Analog multipliers are used for frequency conversion and critical components in modern radio frequency (RF) systems. A mixer converts RF power at one frequency into power at another frequency to make signal processing easier and also inexpensive. A fundamental reason for frequency conversion is to allow amplification of the received signal at a frequency other than the RF, or the audio, frequency.

3. BasicAnalogMultiplier • The signal at the output is the product of the two input signals

4. MultiplierandMixer Mixer is a device used to mix two input signals and deliver an output voltage at frequencies equal to the difference or sum of the input frequencies. Any nonlinear device can do the job of mixing or modulation, but it often needs a frequency selection network which is normally composed as a LC network. Hence a mixer needs at least one non-linearity, such as multiplication or squaring, in its transfer function.

5. MixerDefinitions Mixers are non-linear devices used in systems to translate one frequency to another. All mixer types work on the principle that a large Local Oscillator (LO) RF drive will cause switching/modulating the incoming Radio Frequency (RF) to the Intermediate Frequency (IF) .The multiplication process begins by taking two signals:

6. MixerEquations The resulting multiplied signal will be: This can be multiplied out thus:

7. MixerDefinitions

8. AnalogMultiplierParameters The following parameters are important for an analog multiplier: Conversion Gain: This is the ratio in dB between the IF signal which is the difference frequency between the RF and LO signals and the RF signal. Noise Figure: Noise figure is defined as the ratio of SNR(Signal to Noise Ratio) at the IF port to the SNR of the RF port.

9. Mixersimulations in LabView

10. LabViewBlockDiagramforMixer

11. GilbertCellMixer Two signals V1(t) and V2(t) are applied to a non linear device, which can be characterized by a higher order polynomial function. This polynomial function generates the terms like V1² (t), V2² (t), V1³ (t), V2³ (t), V1² (t)*V2(t) and many others besides the desired V1(t).V2(t). Then it is required to cancel the undesired components. This is accomplished by a cancellation circuit configuration.

12. GilbertCellMixerMathematics It is helpful to study the mathematic basis behind the Gilbert cell. This will help us understand this circuit better, as well as develop an appreciation of the mixing process in general. Let’s define the RF input voltage as

13. GilbertCellMixerMathematics Define the mixing signal: Since this mixing signal is a periodic waveform, we can expand it in this Fourier series:

14. GilbertCellMixerMathematics The Gilbert cell effectively multiplies both of these signals and in the time domain as Giving: where

15. GilbertCellMixerMathematics We have the sum and difference signals present in the output (IF) voltage signal: And all higher-ordered odd harmonics.

16. Multiplierwith OTA A multiplier could be realized using programmable transconductance components. Consider the conceptual transconductance amplifier (OTA) , where the output current is simply given by

17. Multiplierwith OTA Smallsignal is addedtobiascurrent Unwantedcomponenets

18. Multiplierwith OTA Thus, i0(t) represents the multiplication of two signals v1(t) and v2(t) and an unwanted component k2v1(t) . This component can be eliminated as shown in figure

19. Applications of MultiplierIC’s 1)VoltageMultiplication 2)VoltageDivider 3)VoltageSquererandFrequencyDoubler

20. AD633 seriesAnalogMultiplier There is pinouts of AD633 chip in figure There is a basicmultipliercellconnections in figure 2

21. AD633 seriesVoltageMultiplier There is ISIS shematic of AD633 formultiplierconfiguration

22. AD633 seriesVoltageMultiplier Details of signals on analoganalysisformultiplication

23. AD633 seriesVoltageDivider SimilarlytoMultiplicationthere is invertingampifierloopforthat transfer function:

24. AD633 seriesVoltageDivider There is ISIS shematicfordividerconfigurationwith AD633

25. AD633 seriesVoltageDivider Details of signals on analoganalysisfordividing

26. AD633 VoltageSquarerandFrequencyDoubler There is justdifferentconfigurationaboutpins . Weapplysameinputtobothpin as x1 and y1

27. AD633 VoltageSquarerandFrequencyDoubler There is ISIS shematicforfrequencydoublerconfigurationwith AD633

28. AD633 VoltageSquarerandFrequencyDoubler Details of signals on analoganalysisforfrequencydoubling

29. ThankYouForListening.