page_title: Translinear circuit
section_title: 2-Quadrant Multiplier
hierarchical_section_title: Translinear circuit / Example Translinear Circuits / 2-Quadrant Multiplier
caption_attribution_description: English: A biasing scheme for the alternating TL two-quadrant multiplier circuit using diode connections and an EP connection.
context_page_description: A translinear circuit is a circuit that carries out its function using the translinear principle. These are current-mode circuits that can be made using transistors that obey an exponential current-voltage characteristic—this includes BJTs and CMOS transistors in weak inversion. Translinearity, in broad sense, is linear dependence of transconductance on current, which occurs in components with exponential current-voltage relationship.
context_section_description: The design of a 2-quadrant multiplier can be easily done using TLP. The first issue with this circuit is that negative values of currents need to be represented. Since all currents must be positive for the exponential relationship to hold (the log operation is not defined for negative numbers), positive currents must represent negative currents. The way this is done is by defining two positive currents whose difference is the current of interest.
  A two quadrant multiplier has the relationship  hold while allowing  to be either positive or negative. We'll let  and . Also note that  and  etc. Plugging these values into the original equation yields . This can be rephrased as . By equating the positive and negative portions of the equation, two equations that can be directly built as translinear loops arise:
  The following are the alternating loops that implement the desired equations and some biasing schemes for the circuit.
caption: A biasing scheme for the alternating TL two-quadrant multiplier circuit using diode connections and an EP connection.
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