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

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. Basic Analog Multiplier
The signal at the output is the product of the two input signals

4. Multiplier and Mixer
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. Mixer Definitions
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. Mixer Equations The resulting multiplied signal will be:
This can be multiplied out thus:

7. Mixer Definitions

8. Analog Multiplier Parameters
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. Mixer simulations in LabView

10. LabView Block Diagram for Mixer

11. Gilbert Cell Mixer
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. Gilbert Cell Mixer Mathematics
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. Gilbert Cell Mixer Mathematics
Define the mixing signal:
Since this mixing signal is a periodic waveform, we can expand it in this Fourier series:

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

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

16. Multiplier with 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. Multiplier with OTA Small signal is added to bias current
Unwanted componenets

18. Multiplier with 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 Multiplier IC’s
1)Voltage Multiplication 2)Voltage Divider 3)Voltage Squerer and Frequency Doubler

20. AD633 series Analog Multiplier
There is pin outs of AD633 chip in figure
There is a basic multiplier cell connections in figure 2

21. AD633 series Voltage Multiplier
There is ISIS shematic of AD633 for multiplier configuration

22. AD633 series Voltage Multiplier
Details of signals on analog analysis for multiplication

23. AD633 series Voltage Divider
Similarly to Multiplication there is inverting ampifier loop for that transfer function:

24. AD633 series Voltage Divider
There is ISIS shematic for divider configuration with AD633

25. AD633 series Voltage Divider
Details of signals on analog analysis for dividing

26. AD633 Voltage Squarer and Frequency Doubler
There is just different configuration about pins . We apply same input to both pin as x1 and y1

27. AD633 Voltage Squarer and Frequency Doubler
There is ISIS shematic for frequency doubler configuration with AD633

28. AD633 Voltage Squarer and Frequency Doubler
Details of signals on analog analysis for frequency doubling

29. Thank You For Listening.