Gilbert cell

<h2 id="function">Function</h2>
<table><tbody><tr><th></th><th></th><th></th></tr><tr><td>Howard Jones, 1963</td><td>Gilbert, 1968 (beta independent)</td><td>Gilbert, later (beta dependent)</td></tr></tbody></table>
<p>There is little difference between the Jones cell and the translinear multiplier in this topology. In both forms, two <a href="/facts/Differential_amplifier/0MWj8eCR">differential amplifier</a> stages are formed by emitter-coupled transistor pairs (Q1/Q4, Q3/Q5) whose outputs are connected (currents summed) with opposite phases. The emitter junctions of these amplifier stages are fed by the collectors of a third differential pair (Q2/Q6). The output currents of Q2/Q6 become emitter currents for the differential amplifiers. Simplified, the output current of an individual transistor is given by ic = gm vbe. Its <a href="/facts/Transconductance/lwh8krQa">transconductance</a> gm is (at T = 300 K) about gm = 40 IC. Combining these equations gives ic = 40 IC vbe,lo.  However, IC here is given by vbe,rf gm,rf. Hence ic = 40 vbe,lo vbe,rf gm,rf, which is a multiplication of vbe,lo and vbe,rf. Combining the two different stages output currents yields four-quadrant operation.
</p><p>The Jones topology can be generalized by "stacking" any number of pairs of differential pairs (whose two differential inputs and two differential outputs are likewise connected out-of-phase and in-phase, respectively) on top of a conventional Jones cell, resulting in a circuit that retains the balanced nature of the Jones cell's operation. Specifically, the differential output current would now be proportional to the product of an <i>arbitrary</i> number of differential inputs (or some translinear function thereof).<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> However, the utility of this generalization in practical microelectronics settings is limited due to the large voltage headroom needed to keep all of the transistors in the proper (forward-active) <a href="/facts/Bipolar_junction_transistor/9BMcGv5Q">region of operation</a>.
</p><p>However, in the cells later invented by Gilbert, shown in the figure on the right, there are two additional diode-connected transistors (labeled as V1 and V2). This is a crucial difference because they generate the logarithm of the associated differential (X) input current so that the exponential characteristics of the following transistors result in an ideally perfect multiplication of these input currents with the remaining pair of (Y) currents. This additional diode cell topology is typically used when a low distortion <a href="/facts/Voltage-controlled_amplifier/FSUqSByl">voltage-controlled amplifier</a> (VCA) is required. This topology is rarely used in RF mixer/modulator applications for various reasons, one being that the linearity advantage of the top linearized <a href="/facts/Cascode/2fPqtmQQ">cascode</a> is minimal due to the near-square wave drive signals to these bases. The drive is less likely to be a fast-edge squarewave at very high frequencies when there may be some advantage in the linearization.
</p><p>Nowadays, functionally similar circuits can be constructed using CMOS or BiCMOS cells.
</p>
<h2 id="see-also">See also</h2>
<ul>
<li>Electronics portal</li></ul>
<ul><li><a href="/facts/NE612/w6cLWScg">NE612</a>, oscillator, and mixer.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Allen A. Sweet, "Designing Bipolar Transistor Radio Frequency Integrated Circuits", Artech House, 2007, ISBN 1596931280 page 205 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Gavell, Marcus; Gunnarsson, Sten E.; Angelov, Iltcho; He, Zhongxia Simon; Ferndahl, Mattias; Zirath, Herbert (October 2017). "Design and Analysis of a Wideband Gilbert Cell VGA in 0.25- \mu \rm m InP DHBT Technology With DC-40-GHz Frequency Response". IEEE Transactions on Microwave Theory and Techniques. 65 (10): 3962–3974. doi:10.1109/TMTT.2017.2693146. ISSN 1557-9670. <a href="https://ieeexplore.ieee.org/document/7914700" target="_blank">https://ieeexplore.ieee.org/document/7914700</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Jones, Howard E., "Dual output synchronous detector utilizing transistorized differential amplifiers" Archived 2018-03-11 at the Wayback Machine, U.S. patent 3,241,078A (filed:  18 June 1963; issued:  15 March 1966) <a href="http://pdfpiw.uspto.gov/.piw?docid=03241078&PageNum=1" target="_blank">http://pdfpiw.uspto.gov/.piw?docid=03241078&PageNum=1</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Gilbert, B. (December 1968). "A precision four-quadrant multiplier with subnanosecond response" (PDF). IEEE Journal of Solid-State Circuits. SC-3 (4): 353–365. doi:10.1109/JSSC.1968.1049924. S2CID 6584426. Archived from the original (PDF) on 2020-02-18. <a href="https://web.archive.org/web/20200218182255/https://pdfs.semanticscholar.org/f65e/7d9e6c97a701c97d795cff1d363cb6dcdfc9.pdf" target="_blank">https://web.archive.org/web/20200218182255/https://pdfs.semanticscholar.org/f65e/7d9e6c97a701c97d795cff1d363cb6dcdfc9.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Hong, Brian; Hajimiri, Ali (August 2016). "Analysis of a balanced analog multiplier for an arbitrary number of signed inputs" (PDF). International Journal of Circuit Theory and Applications. 45 (4): 483–501. doi:10.1002/cta.2243. S2CID 3621769. <a href="https://chic.caltech.edu/wp-content/uploads/2016/08/BHongMultiplierCTA2016-1.pdf" target="_blank">https://chic.caltech.edu/wp-content/uploads/2016/08/BHongMultiplierCTA2016-1.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
</ol>

Gilbert cell open-in-new

Gilbert cell