A CMOS Multiplied Input Differential Difference Amplifier: A New Active Device and Its Applications

1. Introduction

Active elements play an important role in communication subsystems, measurement, biomedical applications, and many other research areas. Standard active devices [1,2], commonly used in the latest research works, utilize linear operations in inter-terminal defining relations. This means that transfers between input and output terminals are ideally determined by frequency independent constants (voltage-, current-, transconductance-, or transresistance-gain/attenuation), or/and linear mathematic operations (summation or subtraction). The values of these constants can be electronically controlled in many cases. However, communication systems also require nonlinear operations in order to obtain common signal-processing blocks, such as mixers, modulators, etc. Attempts at trying to design these devices, implementing the so-called modular concept of internal structure, i.e., built from basic subparts with standard linear inter-terminal relations (current differencing transconductance amplifier [3], current conveyor transconductance amplifier [2], voltage differencing current conveyor [2,4], for example), have been reported. Devices with at least one nonlinear inter-terminal relation and their application potential, have not been frequently studied (it appears that there are only two works in recent literature [5,6]). The device presented in [6] employs commercially available components (a voltage-mode multiplier and current feedback amplifier). However, the proposed multiplication-mode current conveyor (MMCC) reported in [5,6], has some important drawbacks: (a) the MMCC element does not provide immediate results for the operation of multiplication in the form of current-sourced signal (therefore, it is not suitable for simple and direct creation of electronically controllable inverting/noninverting amplifiers, current-/voltage-mode integrators, etc., with a minimal number of external passive elements); (b) summation/subtraction operations are not directly available in the frame of the designed MMCC device (therefore, employment of the device as part of the chain in multi-feedback systems is much more difficult in the case of filters and oscillators). Our contribution presents an active device for direct providing the operations of multiplication, voltage summing, and subtraction, in a so-called multiplied input differential difference amplifier (MIDDA). A MIDDA addresses the issues previously noted, relating to MMCC elements. Its features are fully utilized in the nonlinear application of a double-sideband amplitude modulator (AM-DSB), that is not directly available with the help of previously reported MMCC elements (additional active circuitry must be included in order to obtain the same function, and therefore the final application is much more complex).

2. A Multiplied Input Differential Difference Amplifier

This active device was developed because of the requirement for electronically controllable active blocks (integrators, amplifiers, etc.), as well as the requirement for devices which provide a nonlinear operation of multiplication that is useful for analogue systems, as previously mentioned. A MIDDA partially operates as a voltage differencing differential difference amplifier (VDDDA), reported in [7,8]. However, the multiplication of signals at the input section is a new feature which is not provided by VDDDA elements. Figure 1 explains the small-signal behaviour of a MIDDA.

Figure 1a includes the block structure of a MIDDA. This topology was preserved in case of implementation using CMOS technology. The first subpart of a MIDDA, depicted in Figure 1a, is indicated by a MLT (multiplier) with a current output terminal. Note that our design was inspired by the solution presented in [9]. However, it was completely redesigned, and supplemented by an input linearization system and a boosting operational transconductance amplifier [1,2]; this is visible in the full transistor structure, shown in Figure 2. When studying our design in detail, it is possible to observe some important differences to [9], as follows: (a) a redesign of the multiplying core, providing better dynamics and using larger bias current, allowing a wider range of the input voltage signal, as well as the speed and frequency bandwidth; (b) input linearizing attenuators, designed to improve applications with linear operations; and (c) an additional operational transconductance amplifier output section, required for the boosting of the output current and overall transconductance. The output operational transconductance amplifier was designed with cascoded current mirrors exhibiting auxiliary biasing (classical cascoded mirrors are not applicable in extremely low-voltage processes because of limited voltage space).

A new solution, which utilizes a CMOS voltage differential difference buffer (VDDB), forming the second subpart of the MIDDA (also shown in Figure 1a), differs from the classical concept of a VDDDA [8]. As becomes obvious when studying the internal structure of the VDDB depicted in Figure 2, the CMOS circuitry is completely different, and much more complex, than the simple structures presented in [7,8]). The key difference is that our solution is based on folded-cascode architecture, and includes both NMOS and PMOS differential pairs. The CMOS process C035 I3T25 (ON Semiconductor) 0.35 μm (3.3 V) was chosen for the design and fabrication of the MIDDA prototype because it was the most suitable technology for our study. Figure 1b shows an overview of the layout of the fabricated device. Unfortunately, a microphotograph is not available due to technologically-unavoidable plating, placed above the fabricated die in I3T technologies. The MIDDA element has four voltage input terminals (Y, X, n, p), one output terminal o, and one auxiliary terminal z. The operation of the device can be defined using the following simple inter-terminal relations: I_z = V_X × V_Y × k, V_o = V_z − V_n + V_p, where k (given by technological constants and dimensions of key transistors in internal structures) can be expressed using:

$$k\cong {\left(\frac{2R_a}{R_b}\right)}^2.\sqrt{2\frac{K_{Pn}}{2}{\left(\frac{W}{L}\right)}_{1,2,3,4}\frac{K_{Pp}}{2}{\left(\frac{W}{L}\right)}_{5,6}}{R}_L.5\sqrt{K_{Pn}4I_{bias1}{\left(\frac{W}{L}\right)}_{7,8}}$$

(1)

Design constants are: K_Pn = 136 μA/V², K_Pp = 29 μA/V², V_thn = 0.6 V, and V_thp = −0.62 V, for NMOS and PMOS in this I3T CMOS technology. The multiplying constant k was obtained from the detailed analysis of the MLT subpart. The first term of (1) represents the contribution of auxiliary linearization and attenuation blocks (components including M_X1,2 and M_Y1,2 with resistors R_a and R_b, as visible from Figure 2). The second term of (1) covers the effect of differential pairs of the multiplying core (transistors M_1–4 and M_5–6 and their aspect ratios), and the conversion of the output current of these transistors, to the differential output voltage of the R_L resistors. The last term (right side of (1)) includes the contribution of boosting the output transconductance amplifier (aspect ratio of M_7,8 and 4I_bias1, derived from I_bias1 through biasing current mirrors, see Figure 2). Constant 5 represents the effect of the current gain of internal mirrors on the boosting transconductance amplifier. Note that a hand calculation of k yields a value of about −2 mA/V², whereas a simulation provides a value of about −1.8 mA/V² (note that the multiplier is inverting in basic configuration). This mismatch is caused by several inaccuracies in the ideal calculation: (a) a non-equal bulk and source voltage V_BS ≠ 0 V for some transistors (differential pairs where bulk terminals are connected to V_DD or V_SS), which impacts the V_th and transconductance of partial specific transistors; (b) the rounding of resistor values (exact value supposes multiplication of 0.975 kΩ/square); (c) a process and temperature dependence of K_P(n,p), as well as partial transconductances of CMOS transistors in proposed topology. The real experimental value of the k parameter equal to −1.3 mA/V², falls into the range of the predicted values from Monte Carlo and corner analyses. The CMOS structure of the MIDDA element, including W/L aspect ratios of all the transistors, values of passive elements, and biasing sources, are shown in Figure 2. Note that not all ESD precautions and bulk connections (NMOS to V_SS, PMOS to V_DD) are included in Figure 2, because of simplicity.

The linear ranges of DC transfer characteristics of the real MLT section are limited up to ±500 mV for inputs X and Y, and up to ±350 μA for the auxiliary terminal z. The examples of measured DC transfer characteristics between input voltage (V_Y) and output current (I_Z), are shown in Figure 3a; V_X serves as the DC constant, driving overall transconductance (in accordance to g_m ≅ 1.3 × 10⁻³ V_X). The gain bandwidth (GBW) of the real prototype overcomes 48 MHz for the MLT subpart of the MIDDA (Figure 3b). The sweep of voltage V_X between ±0.05 and ±0.5 V, causes a change in g_m between ±60 μS and ±660 μS (both polarities of g_m are available by the DC control voltage, in comparison to a standard operational transconductance amplifier [1]), as illustrated by a graph shown in Figure 4. The DC input and output linear range of VDDB reaches approximately ±700 mV (range is valid for inputs z, n, p, and output o), as shown in Figure 5a. The bandwidth (3 dB) of the VDDB part is 45.1 MHz or more, based on the particular configuration (see Figure 5b). Full, detailed information relating to the overall MIDDA performance is summarized in

Table 1. Overall typical performance of MIDDA obtained from the measurements.

CMOS MLT Subpart
Parameter/Transfer from→to
Small-Signal AC Transfer (GBW > 42 MHz)
gm (X→z) (VY = 50→800 mV)	45→974 μS
gm (X→z) (VY = −50→−800 mV)	−80→−2210 μS
gm (Y→z) (VX = 50→800 mV)	60→1030 μS
gm (Y→z) (VX = −50→−800 mV)	−62→−1700 μS
input DC dynamical range
X→z (VY = ±50→±500 mV)	−500→900 mV
Y→z (VX = ±50→±500 mV)	−600→900 mV
harmonic distortion
THDX→z (1 kHz, VY = ±1000 mV)	0.06%→1.08% (for VX = 200→1000 mVpk-pk)
THDY→z (1 kHz, VX = ±1000 mV)	0.08%→1.38% (for VY = 200→700 mVpk-pk)
input/output resistances
RX_DC (any value of VY)	100 MΩ
RY_DC (any value of VX)	100 MΩ
Rz_DC (VY = 50→800 mV)	1 MΩ→176 kΩ
Rz_DC (VY = −50→−800 mV)	3 MΩ→140 kΩ
Rz_DC (VX = 50→800 mV)	66 kΩ→5.2 kΩ
Rz_DC (VX = −50→−800 mV)	107 kΩ→2.4 kΩ
CMOS VDDB Subpart
small-signal AC transfer
Kz→O [−] (−3 dB)	1.02 (55 MHz)
Kn→O [−] (−3 dB)	1.02 (62 MHz)
Kp→O [−] (−3 dB)	1.01 (45 MHz)
input dynamical range
z→o	−800→700 mV
n→o	−700→700 mV
p→o	−1600→1000 mV
distortion
THDz→o	0.04%→0.41% (for Vz = 100→1500 mVpk-pk)
THDn→o	0.07%→0.33% (for Vn = 100→1500 mVpk-pk)
THDp→o	0.03%→0.11% (for Vp = 100→1500 mVpk-pk)
input/output resistances
Rz,n,p	100 MΩ
RO	0.54 Ω

, including the results of the real experiments. It always covers the whole range of tunability for the controllable parameters. Even in the case when characteristics are asymmetrical in positive and negative corners, i.e., limits of linearity in positive and negative polarity are not symmetrical. Note that the ranges mentioned above are valid when symmetrical operation is required, i.e., absolute values of parameters are the same in both polarities in the case of the ranges mentioned above, which are the most useful in practice.

The examples of simple linear and nonlinear operations of the MIDDA are shown in Figure 6. Figure 6a presents the typical DC response of the MLT subpart, producing an output current I_z as a nonlinear parabolic function of the input voltages V_X = V_Y = V_inp. This behaviour can be confirmed in the time domain (Figure 6b), where sine wave excitation creates output current with single polarity (negative due to negative k) and double frequency. Figure 6c,d provide an overview of the linear operation in time domain. The first figure represents the summation V_o = V_p + V_z (Figure 6c), and the second figure provides the results of the operation of subtraction V_o = V_p − V_n (Figure 6d). In both cases, square-wave excitations were provided in order to also present the stability of the device. All of these results confirm VDDB functionality, as well as transient responses for sine wave excitation (Figure 6e). All accompanying details are included in Figure 6.

The proposed MIDDA is beneficial for utilization in linear, and especially nonlinear, applications. When a signal is connected to the Y terminal and a DC voltage is provided to the X terminal, this serves for a tuning of the overall transconductance g_m (k × V_X = g_m), for example, the MIDDA usually operates in the linear applications. Nonlinear applications require a multiplier—both inputs (Y and X) are used for signal operations, as in the case of the AM modulator, for example.

3. Application Examples

The main intention of this paper is to introduce a MIDDA as a new active device, suitable for basic electronically controllable applications (amplifiers, integrators, and other building blocks required in analogue signal processing and circuit synthesis), and also as a building block for providing nonlinear operations. The following text focuses on the simple examples of MIDDA-based applications (controllable voltage amplifiers, controllable lossless integrators, controllable first-order high-pass filters, and double-sideband amplitude modulators). It should be highlighted that the presented building blocks, based on linear signal processing operations (amplifiers and integrators), possess features of electronic controllability in both polarities (they can be simply used in both the noninverting and inverting variant, by a simple change in the polarity of the DC control voltage).

3.1. 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_m = k × V_X, in Figure 7a labeled as V_gm). The second input Y serves as a signal input. Then, the input voltage V_inp transforms through the g_m, to the output current from terminal z of the MLT subpart, and the external resistive 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:

$$K_{V\_ampl}=\pm g_{m}R=\pm k{V}_{gm}R\cong \pm 1.3\cdot {10}^{-3}{V}_{gm}R,$$

(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:

$$K_{V\_\mathrm{int}}(s)=\pm \frac{g_m}{sC}.$$

(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:

$$K_{V\_HP}(s)=\pm \frac{s}{s+\frac{g_m}{sC}}$$

(4)

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_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. Moreover, it provides a low-impedance voltage output in these applications (voltage-controlled integrators, voltage-controlled amplifiers), which is an important advantage in comparison to [5,6].

3.2. 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 kΩ and voltage buffer (for impedance separation of spectrum analyser input having 50 Ω 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:

$$v_o(t)=v_c(t)+v_c(t)\cdot v_m(t)\cdot k\cdot R,$$

(5)

This formula can be modified to:

$$v_o(t)=V_c[1+k\cdot R\cdot v_m(t)]\cos \left({\mathsf{\omega }}_{c}t\right),$$

(6)

where v_m(t) is the general (waveform shape) modulating signal and v_c(t) = V_ccos(ω_ct) represents the carrier wave. For the sine wave, we can rewrite (6) to:

$$v_o(t)=V_c\left[1+k\cdot R\cdot V_m\cos \left({\mathsf{\omega }}_{m}t\right)\right]\cos \left({\mathsf{\omega }}_{c}t\right)$$

(7)

The presence of the product k × 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 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)) × 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 µm), 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.

4. Discussion

Several advanced active devices with a various number of terminals and various principles of controllability have been developed in recent years [10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Recently proposed active devices are compared in

Table 2. Comparison of recently reported electronically controllable advanced multi-terminal active devices (selected examples).

Work	Active Device	No. of Terminals f	No. of Controllable Parameters (Type)	MULTIPLICATIVE Inter-Terminal Relation Available	Device Fabricated as IC
[1,3,10,11,12]	CDTA 1	5	1 (gm) a	No	Yes
[13]	CCCDTA 2	4	3 (Rp, Rn, gm) b	No	No
[14]	MCDTA 3	8	2 (gm1, gm2)	No	No
[15,16]	CCTA 4	4	1 (gm)	No	Yes
[17]	CCCCTA 5	4	2 (RX, gm)	No	No
[18,19]	CFTA, ZC-CFTA 6	4 (5)	1 (gm)	No	No
[4,20]	VDCC, ZC-CG-VDCC 7	6 (7)	2 (RX, gm) 3 (RX, gm, B) c	No	Yes
[21]	DO-VDBA 8	5	1 (gm)	No	No
	FB-VDBA 9	6	1 (gm)
	DO-CG-VDBVA 10	6	2 (gm, A) d
[22]	MCDU 11	5	4 (Rp, Rn, B1, B2)	No	No
[23]	ZC-CCCFDITA 12	6	2 (Rf, gm)	No	No
[7,8]	VDDDA 13	6	1 (gm)	No	No
[5,6]	MMCC 14	4	1 (A) e	Yes	No
this work	MIDDA	6	1 (gm) e	Yes	Yes

¹ Current Differencing Transconductance Amplifier (CDTA); ² Current Controlled CDTA (CCCDTA); ³ Modified CDTA (MCDTA); ⁴ Current Conveyor Transconductance Amplifier (CCTA); ⁵ Current Controlled CCTA; ⁶ (Z-copy) Current Follower Transconductance Amplifier ((ZC)-CFTA); ⁷ (Z-copy Controlled-Gain) Voltage Differencing Current Conveyor (VDCC, (ZC-CG)-VDCC); ⁸ Dual Output Voltage Differencing Buffered Amplifier (DO-VDBA); ⁹ Fully Balanced VDBA (FB-VDBA); ¹⁰ Dual Output Controlled Gain Voltage Differencing Buffered Voltage Amplifier (DO-CG-VDBVA); ¹¹ Modified Current Differencing Unit (MCDU); ¹² Z-copy Current Controlled Current Followed Differential Input Transconductance Amplifier (ZC-CCCFDITA); ¹³ Voltage Differencing Differential Difference Amplifier (VDDDA); ¹⁴ Multiplication Mode Current Conveyor (MMCC); ^a transconductance (g_m); ^b electronically adjustable resistance of single current input terminal (R_X, R_f) or resistances of differential input terminals (R_p, R_n); ^c electronically adjustable current gain (B); ^d electronically adjustable voltage gain (A); ^e available if one of the input voltages of the multiplier section is supposed as the DC constant (if necessary for linear inter-terminal operation); ^f terminals for DC control of parameters not included.

. However, only one of these exhibits the ability to perform multiplication between two input voltages, so acts as our MIDDA concept. MMCC device [5,6] has this operation implemented to voltage transfer between Y and X terminals of current conveyor of second generation (product of voltages from Y₁ and Y₂ terminals is available at X terminal). It may serve for the electronic control of voltage gain (A) between the Y and X terminals. However, as we stated in the introductory part of this paper, the MMCC does not simultaneously provide the results of multiplication in the form of current, and the summation/subtraction operations. Therefore, these limitations further complicate the implementation of the device in building blocks and applications discussed in this paper (for example in the case of the AM-DSB modulator).

5. Conclusions

The MIDDA device presented in this paper offers the following advantageous features, simultaneously: (a) the possibility to construct lossless, non/inverting voltage- or current-mode integrators with electronically controllable parameters, when only one external and grounded capacitor is added (useful for application in linear active filters, oscillators, and other subsystems)—to the best of authors’ knowledge, none of the commercially available multipliers have an accessible output response in the form of current; (b) the nonlinear operation of multiplication is available (for purposes of modulation, demodulation, mixing, shaping, etc., as was proven by this paper); (c) the direct availability of summation/subtraction operations (useful for multi-feedback systems); (d) it excludes utilization of opamp-based differential-summing amplifiers, including floating feedback resistors in the VDDB subpart, see internal structure of AD633, HA2556 , for example, due to a different concept of the CMOS structure; (e) comparable or better features to commercially available solutions (GBW, voltage ranges, offsets), even under lower supply voltages (±1.65 V). The proposed MIDDA device can be easily applied in miniaturized IC solutions for amplitude modulation and demodulation purposes, in long-wave and medium-wave communication systems. In comparison to [5,6], the MIDDA can be easily used for AM-DSB modulation (Figure 9), whereas MMCC suffers from the unavailability of output operation of summation of product of modulation and carrier wave with carrier wave. To the best of the authors’ knowledge, this device is the very first fabricated prototype based on the differential difference principle in the output section, and allows multiplication at the input section simultaneously.

We suppose that the future will see the development of many other (more complex) electronically controlled applications of MIDDA, in the field of harmonic oscillators (the useful methods for their synthesis are discussed in [24] for example), generators, multi-feedback active filters, and active filters, with electronically reconfigurable transfer responses [20,23], immittance converters, etc.