Novel circuit design techniques for bipolar and MOS four-quadrant analog multipliers operable on low supply voltage are described. There are three design techniques for multipliers operable on low supply voltage. One is the transistor-size unbalance technique. Another is the bias offset technique. A third is the multitail technique. Bipolar and MOS four-quadrant analog multipliers proposed in this paper consist of transistor-pairs with different transistor sizes (i.e. emitter areas or gate W/L values are different), transistor-pairs with the same bias offset or multitail cells (i.e. quadritail cells and an octotail cell). Several kinds of squaring circuits consisting of such transistor-pairs are applied to the multipliers when the multiplication method is based on the quarter-square technique. These multipliers all have satisfiable multiplication characteristics with four-quadrant operations in analog signal processing, whether implemented in bipolar technology or implemented in MOS technology.

Circuit design techniques for linearizing adaptively biased differential pairs are described. An emitter-and source-coupled pair is adaptively biased by a squaring circuit to linearize its transconductance, one of whose inputs is divided by resistors. An input signal for a differential pair or a squaring circuit is set to an adequate amplitude by a resistive divider without sacrificing linearity. Therefore, a differential pair is biased by the output current of a squaring circuit and they are coupled directly. There are three design techniques for squaring circuits. One is the transistor-size unbalance technique. Another is the bias offset technique. A third is the multitail technique. The bipolar and MOS squaring circuits discussed in this paper were proposed by the author previously, and consist of transistor-pairs with different transistor size (i.e., the emitter areas or gate W/L values are different), transistor-pairs with the same bias offset, or a multitail cell(i.e., a triple-tail cell or quadritail cell). Several kinds of squaring circuits consisting of such transistor-pairs are applied to produce the quadratic bias currents for compensating the nonlinearity of an emitter-and source-coupled pair. Therefore, four circuits using emitter-coupled pairs with adaptive-biasing current and four circuits using source-coupled pairs with adaptive-biasing current are proposed and analyzed in depth. Furthermore, a circuit configuration for low voltage operation is also introduced and verified with bipolar transistor-arrays on a breadboard.

An emitter–coupled pair with a dynamic bias current and a source–coupled pair with a dynamic bias current are proposed as an exponential–law element and a square–law element that operate as a floating bipolar junction transistor (BJT) and a floating MOS field–effect transistor (MOSFET). In bipolar technology, a hyperbolic sine function circuit and a hyperbolic cosine function circuit are easily obtained by subtracting and summing the output currents of two symmetrical exponential–law elements with positive and negative input signals. In the same manner, an operational transconductance amplifier (OTA) and a squaring circuit are obtained by subtracting and summing the output currents of two symmetrical square-law elements with positive and negative input signals in CMOS technology. The proposed OTA and squaring circuit possess the widest input voltage range ever reported.

This letter describes an MOS operational transconductance amplifier and an MOS four-quadrant analog multiplier using the quadritail cell, which provides an output current proportional to the square of a differential input voltage. As a result, a linear transconductance amplifier and a quarter-squarer multiplier can be obtained in theoretical circuit analysis.

A novel circuit design technique for realizing a linear CMOS transconductance element, consisting of an adaptively biased source-coupled differential pair using a quadritail cell, is proposed. In the circuitry, the quadritail cell, which provides an output current proportional to the square of a differential input voltage, cancels a nonlinear term of the source-coupled differential pair. The circuit have a superior linearity and a wide linear input voltage range compared with the conventional linear CMOS transconductance elements because the transconductance characteristic is theoretically linear over wide input voltage range when all the MOS field-effect transistors (MOSFETs) are operating in the saturation region and the MOSFETs' behaviors are according to the relation based on the square-law characteristic. The proposed adaptively biased source-coupled differential pair was verified by using transistorarrays and discrete components on a breadboard.

A novel circuit design technique for bipolar linear transconductance amplifiers is presented. A triple-tail cell, which consists of three emitter-common transistors biased by a single tail current, is exchangeable with an emitter-coupled pair in the multi-tanh cell, such as a multi-tanh doublet, a multi-tanh triplet or a multi-tanh quad. Therefore, the multi-tanh technique is further theoretically expanded to the super-multi-tanh technique. In this paper, the super-multi-tanh technique is proposed and discussed, and furthermore, a super-multi-tanh doublet is verified with bipolar transistor-arrays and discrete resistors on a breadboard.

A bipolar low-voltage multiplier core is presented. The proposed low-voltage multiplier core is built from a bipolar quadritail cell. Voltages applied to the individual bases of the transistors in the bipolar quadritail cell are aVxbVy, (a1)Vx(b1)Vy ,aVx(b1)Vy, and (a1)VxbVy, where Vx and Vy are the input signals, and a and b are constants, for example, VxVy, O, Vx, and Vy. Simple input systems using resistive dividers are also described. The dc transfer characteristics were verified on a breadboard using transistor-arrays and discrete components. The dc transfer characteristic of the proposed multiplier core is very close to that of the Gilbert multiplier cell, but the proposed multiplier core is operable on low supply voltage. Therefore, a bipolar multiplier core using a quadritail cell is a low-voltage version of the Gilbert multiplier cell. The proposed bipolar multiplier is practically useful because it can be easily implemented in integrated circuits by utilizing a multiplier core and a resistor-only input system, and it also operates at very lowvoltage. Therefore, the proposed bipolar multipliers are very suitable for low-power operation.

Novel circuit design techniques for CMOSFET (complementary MOS field-effet transistor)-only bias circuits, which each include a current mirror with a peaking characteristic, a current reference with a positive temperature coefficient, and a voltage reference with an optional temperature dependence, are described. An MOS Nagata current mirror is analyzed, and bias circuits like a CMOS self-biasing Nagata current reference and a CMOS self-biasing Nagata voltage reference, both of which include an MOS Nagata current mirror, are discussed. In addition, a CMOS temperature coefficient shifter, used to add an offset voltage and an optional temperature coefficient to a reference voltage, is also discussed. The CMOS Nagata voltage reference was verified with a breadboard using discrete componente and a 0.15 mV/ temperature dependence.