1 6.012 - Microelectronic Devices and Circuits Fall 2009 - 11/19/09 handout The marvelous CASCODE: V-V+Q2Q1vout-RL+RSvS+-cascode ≡ a two-transistor configuration formed of a common-emitter/-source stagefollowed by a common-base/-gate stage The cascode is a very useful two-transistor stage thatprovides the performance of a common-emitter/-source stage with a much smaller Miller effect and much largeroutput resistance. The stage was first introduced to get better high-frequency performance, and the higher output resistance was viewed as a bonus; now designers takeadvantage of both features in a variety of situations. Miller Effect: Using a common-base/-gate stage, with its low inputresistance, to load a common-emitter/source stage meansthat the voltage gain of the latter stage will be small, andso it will have a greatly reduced Miller effect. It will still have the same high input resistance and large current gainas before, however.2 The common-base/-gate member of this pair does notprovide any additional current gain (i.e., its current gain isone), but it does provide voltage gain (as much as, or morethan, a similarly biased common-emitter/-source stagedriving the same load). It also has a very large outputresistance. Together the cascode combination has the same overall current and voltage gains of a common-emitter/ -source stage, the same input resistance, and a largeroutput resistance (see below).1 Output resistance: Consider the circuit sketched on the preceding pagewith zero signal input; apply a test voltage, vt, to theoutput terminals and calculate the resulting current, it, to find the output resistance, Rout ≡ vt/it. The small signallinear equivalent circuit is shown below (RL has not been included; it is in parallel with this Rout): go2gm2v!2vs = 0vt+-go1gm1v!1v!1g!1+-itg!2v!2 = 0+-RS+-We see immediately that it = - (go2 + gπ1) vπ, and at the one node in the circuit we can write vπ (go2 + gπ1) + gm1 vπ + go1 (vt + vπ) = 0 1The voltage gain is actually larger also because of the increased output resistance.3 We solve this for vπ, substitute the result into the expression for it, and find Rout to be: go1 + go2 + gπ1 +gm1 Rout = go1 (go2 + gπ1) To see what this means, notice that if go1 and go2 are much smaller than gπ1, the numerator is approximately (β + 1) gπ1, and the denominator is approximately go1 gπ1, so we have (β + 1)Rout (bipolar cascode) ≈ go1 = (β + 1) ro1 This result is valid for a bipolar cascode. For a MOSFET cascode the small signal model is the same as long as vbs is zero on both devices,2 however gπ1 is zero for a MOSFET so the approximation for Rout is different. The numerator is now approximately gm1, and the denominator is go1 go2,leading to K2Rout (MOSFET cascode) ≈ gm1 = K1 Av,oc2 ro1 go1 go2 where Av,oc2 is the open-circuit voltage gain of Q2. The point is that Rout is again much larger than ro1. Applications: Cascode connections are often used as the gainelements in amplifier stages when the Miller effect is an issue. They are also used in current sources and as non-linear loads where the output resistance of a single 2 For a more general solution see the course text ("Microelectronic Devices and Circuits"by C. G. Fonstad, Jr.), Section 12.5.2.4 transistor is not sufficient.3 As devices are made smaller and smaller, to make them faster and faster, the outputresistance often suffers (i.e., the Early voltage is smaller),and the cascode connection offers a way of recoveringsome of the lost performance. The down side: The "costs" of using a cascode are that you must usetwo transistors instead of one (not a big cost in an integrated circuit) and, more importantly, that there is alarger voltage drop across the pair of transistors in thecascode than there is in a single-transistor stage. This mayreduce the ranges of voltages over which an amplifierusing cascodes will operate. This is particularly importantin modern circuits designed to use relatively low supplyvoltages and they consume minimal amounts of power(for cellular telephone applications, etc.). 3 Examples of cascode current mirrors can be seen in Figures 12.19 and 13.20 of thecourse text ("Microelectronic Devices and Circuits" by C. G. Fonstad, Jr.).MIT OpenCourseWarehttp://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Fall 2009 For information about citing these materials or our Terms of Use, visit:
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