A β-error elimination in the translinear reduction of the "log-antilog" multiplier/divider

Abstract

A new t p e of the one-quadrant analog multipiYer/divider based on the translinear reduction of the Vog-anMog" (TLRLA) mdt~plier/dir.ider circuit is presented in this paper. A new techniquc for the error elimination due to the finite crnrrent gain $ of the used bipolair junction transistors (BJTS) is described. By ai fding seven BJTs (three emitter followers and two simple current mirrors) to the classical TLRLA rnuklpfier/divider, a significant impro vement in xcuracy is achieved. The lineiwity error is smaller than 0.45 % of full scale, and rehtive error is smaller than 1.2 % of fuil scale? in the 0 A to 3 mA input current range? and in the 0 A to 9 mA output current range. These simulated results have been achieved with a 3 Vsupply.

On frequency response and stability of an optical front–end with variable‐gain current amplifier using a bipolar junction transistor translinear loop

“…• The largest gain peaks occur for larger transimpedances T (for smaller control current I C2 ) in 0.35 mm SiGe than for the transimpedances T (for control currents I C2 ) in 0.6 mm Si. These conclusions completely confirm the predictions of Equations (8)- (12), with corresponding MATLAB simulations shown in Figures 6-15. In other words, in the case of the proposed OFE with variable transimpedance using VGCA with BJT TLL, the chip in a cheaper technology with worse BJT parameters (0.6 mm Si) possesses a much better frequency response and stability than the chip in a more expensive technology with better BJT parameters (0.35 mm SiGe).…”

“…Consequently, because the control current I C2 flows through the BJT Q 6 , the current gain b 6 of the BJT Q 6 is nearly constant. The influence of the finite current gain b of the BJTs used can be avoided by applying the approach presented in [12]. The capacitance C x at the input of the VGCA shown in Figure 4 is C x %C Iin.…”

“…In Equations (8)- (12), the meaning of the parameters is the following: g m4 = I C1 /V T , g m5 = I IN /V T , g m9 = I C2 /V T , and g m10 = I OUT /V T are the tansconductances of the BJTs Q 4 , Q 5 , Q 9 , and Q 10 , respectively, V T is the thermal voltage, r p4 = b 4 /g m4 and r p5 = b 5 /g m5 are the input resistances of the BJTs Q 4 and Q 5 , respectively, b 4 is the current gain of the BJT Q 4 , r ce4 = V A /I C1 is the output resistance of the BJT Q 4 , V A is the Early voltage. Because of the constant control current I C1 flowing through the BJT Q 4 , the current gain b 4 is constant, unlike the current gain b 5 .…”

“…Because of the constant control current I C1 flowing through the BJT Q 4 , the current gain b 4 is constant, unlike the current gain b 5 . The influence of the Early voltage V A and the current gain b on the natural frequency o 0VGCA (Equation (9)) and the factor Q VGCA (Equation (10)) is visible from the Equation (12). On the other hand, the influence of the unity gain frequency f T of the BJTs is indirectly related, through the influence of the equivalent capacitance C b10 at the base of the BJT Q 10 .…”

“…The AC transimpedance T(s) = v out /i pd of the OFE can be expressed as T(s) = A VGCA (s)T CVC (s), where A VGCA (s) is the transfer characteristic of the VGCA given by Equations (8)- (12) and T CVC (s) = v out /i cvc is the AC transimpedance of the CVC [6]. Because of the relatively small output capacitance of the VGCA C z (~10 fF), the gain peaking reduction (0.5 < Q CVC < 0.707) of the transfer characteristic T CVC (s) by inserting the feedback capacitor of small capacitance C fb [6] does not significantly affect the double-pole frequency f 0CVC = o 0CVC /2p of the CVC's transfer characteristic T CVC (s), which can achieve high values.…”