Politecnico di Torino Master Degree in Electronic Engineering Analog and Telecommunication Electronics course Prof. Del Corso Dante Miniproject: “ Switched Capacitor: working principles and real IC-device application ” Student Name: Paolo Vinella Student ID: s206827 1 [email protected] Contents 1. Switched Capacitor basics ......................................................................................................... 3 1.1 Realizing a resistor inside integrated circuits ............................................................................. 3 1.2 The need of replacing traditional resistors with Switched Capacitor ........................................ 4 1.3 Switched Capacitor basic element .............................................................................................. 4 1.4 Switched Capacitor working principle: a resistor-like device ..................................................... 5 1.5 Switches: which device? .............................................................................................................. 6 2. Switched capacitors in basic Filters ........................................................................................ 7 2.1 Passive I order Low Pass RC cell ............................................................................................... 7 2.2 Active Integrator (I order Low Pass cell) .................................................................................. 8 2.3 Active Integrator Stray Insensitive .......................................................................................... 12 3. Commercial Active Filter: TI MF10 .......................................................................... 14 3.1 Introduction and key parameters ............................................................................................. 14 3.2 Main circuital building block: State Variable Filter ................................................................ 15 3.3 Basic circuit description............................................................................................................ 16 3.4 Design hints common summary ................................................................................................ 19 3.5 Modes of operations: design example with MODE#3.............................................................. 20 3.6 Recall on BP, LP, HP responses and parameters .................................................................... 22 3.7 Offset contribution .................................................................................................................... 24 3.8 Design of Fourth Order Chebyshev LP filter: using the entire MF10 ..................................... 25 4. Traditional vs Switched Capacitor Filter: which is better? ............................................ 27 5. Final remarks on Switched Capacitor Filters ..................................................................... 29 References ........................................................................................................................................ 30 2 [email protected] 1. Switched Capacitor basics 1.1 Realizing a resistor inside integrated circuits Resistors are one of the basic building blocks for any analog or digital integrated circuit. They play an essential role (as voltage dividers, current regulators,…) and cannot be avoided during design. Inside integrated circuits realized employing silicon (but not only), a resistor can be realized with a doped semiconductor area: we refer to Diffused Integrated Resistor, which exploit the microscopic Ohm’s Law. In fact, an uniformly doped area connected with other devices through ohmic metallic contacts, can be seen as a resistor. Consider an n-doped volume with doping concentration ND, with physical dimensions L x W x t: t = f ( μ , ND ) n W ρ L Recalling the definition of resistivity: 1 1 ρ= = σ q μnND The sample can be seen as a resistor whose resistance is given, as well known, by the relation: L ρ L R=ρ = W t t W Defining the layer resistance R□, which is given by manufacturing, as: ρ R□ = t We can express then the equivalent associated resistance R of the device as: L R = R□ W From the manufacturing standpoint, this is realized considering n squares each of which characterized by R□, putting them in series: 3 [email protected] 1.2 The need of replacing traditional resistors with Switched Capacitor Nowadays, within integrated circuits, where physical layout, space and lithography constrains allow more and more restrictive, this approach is very space (surface) consuming. Realizing integrated circuits, the area occupied by a capacitor is far smaller than the one required by a traditional resistor. In order to make resistor integration still possible and try to overcome this limitation, another approach, completely different, can be used: the Switched Capacitor technique. It is based on the use of a capacitor driven alternatively by a couple (or more) switches between power supply sources. In a MOSFET-oriented IC, realizing a capacitor is not a big deal, since the same technique used to realize the MOS gate area can be used. 1.3 Switched Capacitor basic element The Switched Capacitor is based on two metal plates (realized with polysilicon, a strongly doped silicon sample) separated by a thin oxide layer. Although the structure is a “pure” capacitor, however we must take into account the presence of nonlinearities: • C1 is the ideal desired capacitance; • CP1 and CP2 are the two parasitic terms introduced by the structure, between which especially the second one, associated to the bottom oxide plate which separates the structure from the substrate, can be quite large: even up to the 20-30% in respect to C1! 4 [email protected] 1.4 Switched Capacitor working principle: a resistor-like device Switched capacitor is a technique commonly used to realize filters (but not only) within integrated circuits, which allows to emulate the behavior of a resistor whose resistance is function of the clock frequency used to drive the device. Consider this basic series circuit: R I V1 V2 Assuming V1 > V2, we can write: V1 - V2 I = R Let us now consider a similar system but composed by a capacitor of value C and two switches in counter phase S1 and S2, connecting alternatively the capacitor to either V1 or V2: S1 S2 I V1 C V2 We can easily derive that: S1 CLOSED S1 OPENED Q 1 = C ∙ V1 Q = C ∙ V S2 OPENED S2 CLOSED � ⟶ � ⟶ 2 2 The variation of charge is thus: ∆Q = Q 1 - Q 2 = C ∙ (V1 - V2) We can see ∆Q as the variation of the quantity of charge transferred from V1 to V2. The associated current I is the quantity of charge transferred / second, thus we can divide by the time T which represents the cycle duration: ∆Q C (V1 - V2) I = = = C (V - V ) f T T 1 2 CLK Comparing this result with the formula: V1 - V2 I = R We find the equivalent resistance of the system: REQ 1 I12 R = EQ 1 2 C fCLK 5 [email protected] Example: C=5pF ; fCLK=100kHz REQ= 2MΩ : very high value with very low capacitor (with traditional approach, instead, huge amount of silicon area would be required!). ⟶ The formal definition for Switched Capacitor working principle can be expressed as: “A capacitor, connected alternatively between two low-impedance points (two voltage sources) driven by two switches, behaves like a resistor put in between these two points”. The system works with two switches: for this reason, we talk about sampled system. In order to make the system behave “as” an ideal resistor, keeping an high confidence for the ideality of the equivalent component, we have to use the device with signals at frequency fS << fCLK . In order to keep everything work as it should, the switches S1 and S2 are driven by two square waves Φ1 and Φ2 (digital signals) not overlapped: S1 Φ1 ⟶ S2 Φ2 ⟶ 1.5 Switches: which device? In order to realize the driving switches, the basic idea is the use of a single nMOS or pMOS: Φ Φ Φ We can do even better, employing a transmission gate, based on an nMOS in parallel with a pMOS, which ensures low ON resistance (basically when the switch is closed, it behaves “almost” like a short circuit, with a negligible voltage drop across it). Driving voltage is again a square wave Φ: Φ Φ It is possible to show that the ON conductance of the device, when it is turned “ON” (ohmic region for both nMOS and pMOS) is very low, and equal to: Wn Wp ≐ GON = K VAL - Vtn + Vtp , having defined K Kn = μnCOX = Kp = μpCOX Ln Lp The switch also� ensures low VDS dependence� (better linearity). MOSFET are good switches: off resistance near GΩ range; on resistance several tenth of Ω (depending on transistor sizing). 6 [email protected] 2. Switched capacitors in basic Filters The presence of switched capacitors to replace the resistor(s) within filters, both passive and active (based on OPAMPs) enables the implementation of filters as fully integrated circuits. In fact: • The capacitor that replaces the resistor, together with its switches, offers a more compact structure (less occupation area); • Typically, in filters what counts is the ratio between values rather than absolute ones (for example: C1/C2), allowing to work with small value of capacitances. In fact, we work with a single type of component, and only a good matching (desired ratio) is required. • Error on an absolute value of a parameter can reach up to 30% (tolerance), while error of ratio of values of capacitances can be reduced even to 0.1%! • In