# A CMOS Multiplied Input Differential Difference Amplifier: A New Active Device and Its Applications
## 3 Application Examples
### Simple Linear Applications (Linear Operation)  
A simple circuit, representing a voltage-controlled voltage amplifier, is shown in Figure 7a. This amplifier is formed by using the MLT subpart of the MIDDA. This subpart creates a linear operation (\(V_{X}\) input voltage serves for DC control of transconductance \(g_{\text{m}}=k\times V_{X}\), in Figure 7a labeled as \(V_{\text{gm}}\)). The second input \(Y\) serves as a signal input. Then, the input voltage \(V_{inp}\) transforms through the \(g_{\text{m}}\), to the output current from terminal \(z\) of the MLT subpart, and the external resistive  
Figure 6: A comparison of the simulated and measured examples of MIDDA nonlinear and linear basic operations: (**a**) MLT subpart DC transfer response of \(I_{z}\) at z terminal for \(V_{X}=V_{Y}\), i.e., squaring function; (**b**) MLT subpart transient output response \(I_{x}\) at z terminal; (**c**) VDDB subpart transient response of \(V_{o}\) at terminal o for summation \(V_{o}=V_{p}+V_{z}\) of two square waveforms; (**d**) VDDB subpart transient response of \(V_{o}\) at terminal o for subtraction \(V_{o}=V_{p}-V_{n}\) of two square waveforms; (**e**) VDDB subpart transient response of \(V_{o}\) at terminal o for subtraction \(V_{o}=V_{p}-V_{n}\) of two sine waveforms (measured only). load (\(R\)) provides a conversion of the current, back to voltage. The VDDB subpart serves as a simple voltage follower. The most important benefit of this application is its simple and immediate ability to change the polarity and value of the voltage gain by DC control voltage, very high input impedance, low output impedance, and a single grounded external passive component. The ideal value for the voltage gain of this amplifier can be determined as:  
\[K_{V\_ampl}=\pm g_{m}R=\pm kV_{gm}R\cong\pm 1.3\cdot 10^{-3}V_{gm}R, \tag{2}\]  
where gain range, dynamics, and frequency features, depend on an appropriate selection of value of external grounded resistance (\(R\)). Another possible application of a MIDDA is in a voltage-controlled lossless voltage integrator (Figure 7b). It is obtained by a simple change of the resistor (\(R\)), to a capacitor (\(C\)), as is obvious when comparing Figure 7a,b. This integrator is described in the following equation:  
\[K_{V\_int}(s)=\pm\frac{g_{m}}{sC}. \tag{3}\]  
This integrator has benefits that are similar to those of the voltage-controlled voltage amplifier discussed above. The benefits of both circuits in Figure 7 are not available in standard opamp-based solutions. The last of the presented applications using linear signal processing is a first-order high-pass filter (Figure 8), directly allowing electronic tuning of the cut-off (pole) frequency. This application was obtained from previous topology, through the addition of simple feedback from the output, to terminal \(Y\), and also by full utilization of the VDDB subpart. The symbolical transfer function has the following form:  
\[K_{V\_HP}(s)=\pm\frac{s}{s+\frac{3m}{sC}} \tag{4}\]  
Figure 8: Simple application of a proposed MIDDA in a first-order high-pass filter with adjustable pole frequency. Figure 7: Simple applications of a proposed MIDDA having voltage-controlled transfers in both polarities: (**a**) Voltage-controlled voltage amplifier; (**b**) Voltage-controlled lossless integrator. Note that the filter can be configured as one which is either noninverting or inverting, when inputs \((n,p)\) are interchanged, however, in case of the controllable voltage amplifier and voltage-controlled lossless integrator, polarity is controlled directly by the control voltage \(V_{\mathrm{gm}}\) (see Figure 7). The basic electronically controllable building blocks discussed above (for example integrators), are simple because of the direct implementation of the current output of the MLT subpart in the frame of the MIDDA, which allows it to omit at least one additional passive element.