# A CMOS Multiplied Input Differential Difference Amplifier: A New Active Device and Its Applications
## 3 Application Examples
### Simple Nonlinear Application (Nonlinear Operation)  
The double-sideband amplitude modulator (AM-DSB) has been obtained by utilization of both the multiplicative and summing operations of the MIDDA, as illustrated in Figure 9. The presented solution also contains one resistor (\(R=1\) k\(\Omega\) and voltage buffer (for impedance separation of spectrum analyser input having 50 \(\Omega\) impedance)). Both of these supplementary components are present in the form of simple external parts. The modulating sine wave \(v_{m}(t)\) has an amplitude of \(V_{m}=200\) mV, with a frequency of \(f_{m}=500\) kHz connected to input \(Y\), as an example. The carrier signal \(v_{c}(t)\), with an amplitude of \(V_{c}=250\) mV, and a frequency of \(f_{c}=5\) MHz, feeds into the input terminal \(X\) and auxiliary terminal \(p\), simultaneously. A description of the operation will now be given (also shown in Figure 9b). The modulating wave signal \(v_{m}(t)\) is multiplied with the carrier wave \(v_{c}(t)\), and their product is available at the z terminal of the MLT subpart, in the form of voltage (after conversion of output current from the z terminal, to voltage, through the grounded resistor \(R\)). Following this, the VDDB subpart creates a summation of the carrier wave \(v_{c}(t)\) with the product from the MLT subpart. The output voltage of the modulator is available in the simple form:  
\[v_{o}(t)=v_{c}(t)+v_{c}(t)\cdot v_{m}(t)\cdot k\cdot R, \tag{5}\]  
This formula can be modified to:  
\[v_{o}(t)=V_{c}[1+k\cdot R\cdot v_{m}(t)]\cos(\omega_{c}t), \tag{6}\]  
where \(v_{m}(t)\) is the general (waveform shape) modulating signal and \(v_{c}(t)=V_{c}\cos(\omega_{c}t)\) represents the carrier wave. For the sine wave, we can rewrite (6) to:  
\[v_{o}(t)=V_{c}[1+k\cdot R\cdot V_{m}\cos(\omega_{m}t)]\cos(\omega_{c}t) \tag{7}\]  
The presence of the product \(k\times R\) (\(R\) especially, \(k\) is technological constant) in the equations noted above can be used for variation of the amplitude ratio between modulation and the carrier wave. A similar effect can be observed when the simple attenuator between the input of carrier wave and  
Figure 9: Simple nonlinear application of a proposed MIDDA—AM-DSB modulator: (**a**) circuit implementation; (**b**) explanation of operation of modulation.  
\(p\) terminal is used. The features of this particular application of a MIDDA were verified experimentally. The results are shown in Figure 10. The modulation depth \(m\) obtained for the selected value of \(V_{m}\) and \(V_{c}\) (Figure 10a) reaches 25% (\(m=(V_{o(\max)}-V_{o(\min)})/(V_{o(\max)}+V_{o(\min)})\times 100\)). A measured output spectrum is shown in Figure 10b. It can be seen that suppression of the closest spurious higher harmonics is above 47 dB. Overall power consumption of the MIDDA-based modulator is only 17 mW. Note that if the MIDDA is designed using more up-to-date technology (CMOS technology smaller than 0.35 \(\upmu\)m), its power consumption is lower, however, its dynamic range available for signal processing is also significantly decreased. Therefore, the selection of a particular technology represents a trade-off that has to be accepted.