HIGH FREQUENCY FILTER DESIGN

Transcription

1 HIGH FREQUENCY FILTER DESIGN for High-Frequency Circuit Design Elective by Michael Tse Septeber 2003

2 CONTENTS. Introduction. Types of filters.2 Monolithic filters.3 Integrators.4 Siple first-order g-c filters 2. Filter Design for High Frequencies 2.0 Introduction to filters (separate notes) 2. Special requireents for HF 3. G-C Filter Synthesis 3. Cascaded biquads 3.2 Signal flow graphs 4. Realization of Transconductors 4. BJT transconductors 4.2 MOSFET transconductors 4.3 Exercise Michael Tse: HF Filter Design 2

3 . INTRODUCTION Basic fors: LC-Ladders Due to the advent of op-aps, ACTIVE RC filters becae popular. Miniaturization leads to IC filters which use onolithic technology for active coponents and thin-fils for frequency deterining coponents (C,R). IC onolithic filters becae popular. Advantages: Less coponents, saller volue Good atching of coponents Autoatic tuning correct transfer functions for process/tep variations Saller parasitic caps on chip Fabricated in large quantity Michael Tse: HF Filter Design 3

4 . Types of Filter Realizations Digital filters Analog discrete-tie filters Analog continuous-tie filters.. Digital filters: Signals need to be discretized and digitized, i.e., sapled and converted to digital words, and the filtering is done in the digital doain...2 Analog discrete-tie filters Signals are discretized but NOT digitized. They are called sapled-data. Filtering is done directly to the sapled-data. Exaple: switched-capacitor filters (SC filters) But SC filters are ainly for low-frequency applications (audio range) Discretization (sapling) D/A Digitization (A/D) Filter or Processor Michael Tse: HF Filter Design 4

5 ..3 Analog continuous-tie filters Continuous analog signals are directly processed without any A/D or D/A conversions, sapled-&-hold, anti-aliasing filters, etc. Because of the continuous-tie nature, analog continuous-tie filters are very suitable for high-frequency and high dynaic range applications. Disadvantages:. Sensitive to process and teperature variations 2. Aging 3. Need tunings of the frequency deterining coponents Since we are dealing with high-frequency design, we will focus on Analog Continuous-tie Filters in these notes Michael Tse: HF Filter Design 5

6 .2 Monolithic Filters Fully integrated analog continuous-tie filters were possible when autoatic tuning of coponents becae available, starting 970 s..2. Bipolar filters Properties. High voltage gain.2.2 MOS filters 2. High output drive Properties 3. High frequency (up to ~00 MHz). Low power 4. Low noise and offsets 2. High packing density 3. High noise iunity 4. Ease of design 5. Ease of scaling 6. High frequency (up to ~00 MHz) Michael Tse: HF Filter Design 6

7 .3 Integrators (Building Blocks) Integrators are needed in all active filters. [ In passive filters, integrators are provided by inductors and capacitors, in both I and V doains. ] However, for active filters, only C exists. Hence, we need to have integrators of output/input variables are in the sae voltage or current doain..3. Active RC (Op-ap RC) Integrators V j C j... n x R x C C int M i R i n V o = - - jwc int R i i= V i  C j V j j= C int V i R i V o osfet in triode region to siulate a resistance Michael Tse: HF Filter Design 7

8 Active RC Integrators (con t) The RC integrator shown previously in not very suitable for onolithic realization because the tie constant t i = R i C int cannot be tuned after realization! Note that C and R can only be fabricated with an accuracy of 20% and 5% respectively. With MOSFET-C integrators, the tuning proble can be solved by varying the gate voltage of M i --> R i --> t i. Design notes:. Nonlinearity of MOSFETS is ainly second-order. Thus, MOSFET-C integrators ust be designed in BALANCED FORM in order to cancel even haronics. 2. It is difficult to ipleent good MOS op-aps. Usually, BiMOS technology is used for MOSFET- C integrator filters. 3. It is also possible to tune the frequency using the transconductance instead of the MOSFET resistance. Michael Tse: HF Filter Design 8

9 .3.2 Transconductance-C or g-c Filters BASIC CIRCUIT: The general g-c integrator: V i transconductance g V o = i = V i g n g i V  i i= jwc eff where C eff = C int V j V i  C j... g i g C j V j j= C eff C int x C n x g ÂC j j= Michael Tse: HF Filter Design 9 V o We can control t i = C eff /g i by tuning the transconductance. Note: The transfer function suffers fro loading effects, which depend on the suation cap C j. The gain g is a design paraeter (whereas in active- RC, the op-ap gain doesn t atter).

10 .4 Siple First-order g-c Filters The basic transfer function is: H(s) = V out V in = k s k 0 s w 0 G-C realisation: V in C X g C g 2 A V out The nodal equation is: g V in sc X (V in -V out ) - sc A V out - g 2 V out = 0 Ê C ˆ s X Á V out C = A C Ë X Ê g ˆ Á C A C Ë X V in Ê g ˆ s 2 Á Ë C A C X The paraeters are adjusted by C X = k C A - k for 0 k < g = k 0 (C A C X ) g 2 = w 0 (C A C X ) Michael Tse: HF Filter Design 0

11 2 FILTER DESIGN FOR HIGH FREQUENCIES 2. Special Requireents for HF V a V b g g g g V o = g sc (V a -V b ) C g (a) No nodes with an undesired capacitance to ground. I = g (V a -V b ) parasitic NOT SUITABLE FOR HF In VHF, parasitic caps becoe significant and quite siilar values to the designed capacitances. Thus, we need to ake sure that each node in the filter MUST have a desired capacitance to ground so that we know what it is and how it is put in the transfer functions. V a V b g g g g Michael Tse: HF Filter Design C V o = g sc (V a -V b ) I = g (V a -V b ) SUITABLE FOR HF

12 2. Special Requireents for HF (con t) (b) Balanced operation for reducing even haronics and crosstalks. Signal inversion can be obtained easily in g-c. Balanced transconductance: V c 2 V in V c - 2 V in g g C C V c g Ê V a -V Á b sc Ë 2 ˆ V c is cancelled! V c - g Ê V a -V b ˆ Á sc Ë 2 V c V c 2 Vin 2 V in g I on = I = op g V in 2 g V in 2 I out,diff = I op I on = g V in g g I = g ( 2 V a -V b ) I = - g ( 2 V a -V b) Michael Tse: HF Filter Design 2

13 2. Special Requireents for HF (con t) (c) Sensitivity ust be LOW for coponent variations to reduce errors. In VHF filters, the capacitors are sall and will have 20-00% part of parasitic cap. Hence, inaccuracy is expected in capacitance ratios. Fortunately, ratios of g are usually integer nubers, atching between g s should be good. Thus, sensitivities of filter transfer functions to capacitor values MUST BE KEPT LOW. (d) Dynaic range is deterined by dynaic range of g dynaic range of filter structure e.g., if internal node signal levels have large variations (swings), then the output swing becoes restricted. This usually requires coputer siulations for optiisation. Michael Tse: HF Filter Design 3

14 3. G-C FILTER SYNTHESIS. Cascaded biquad 2. Signal flow graph 3. State space ethod 4. Gyrator ethod BIQUAD: circuit realizing a general filter transfer function of second order H(s) = K a 2s 2 a s a 0 s 2 s w o Q p w o a 2 = a = 0 --> LOWPASS a 2 = a 0 = 0 --> BANDPASS a = a 0 = 0 --> HIGHPASS a = 0 --> BANDSTOP Michael Tse: HF Filter Design 4

15 3. Cascaded Biquads General biquad section using g-c realization (VHF applications) V a g g g V b g 4 V c C 3 C g C 2 V o = where Ê Á C 3 Á C 2 C Á 3 Á s 2 s Ë w o = s 2 V c s g 4 V C b g 3g 5 3 C C 3 g g 2 C (C C 2 ) g 3 C 2 C 3 Q p = C 2 C 3 C g g 2 g 3 V a g g 2 C (C 2 C 3 ) ˆ So, K, a 0, a, w o and Q p can be chosen by choosing g s and C s. Michael Tse: HF Filter Design 5

16 3. Cascaded Biquads (con t) Features:. This biquad is suitable for very high frequencies because each node has a known capacitance to ground. 2. C 2 is not essential, but is unavoidable. Hence, it ust be taken into account. 3. Cascading ultiple biquads will cause loading effects, which ust be taken into consideration because there is no ideal buffer at high frequencies. 4. Output level can be scaled for optial dynaic range by varying K. High order filters: biquad biquad2 Disadvantage of cascaded biquads: Passband sensitivity to coponent variations tends to be too large for soe applications. (A better approach is to start with LC ladder.) Michael Tse: HF Filter Design 6

17 3.2 Signal Flow Graph Synthesis The starting point is passive lossless LC ladder. The following is a 3rd order elliptic low-pass filter. I L3 L 3 The state equations: State V C2 : sc 2 V C2 I L3 I C3 = I V in R I V C2 I 3 I C3 C 2 C 3 C 4 I 5 V C4 R 5 V out sc 2 V C2 I L3 sc 3 (V C 2 -V C4 ) = V in-v C2 R (sc 2 sc 3 )V C 2 - sc 3 V C 4 V C2 R = V in R - I L3 V C2 V C 2 s(c 2 C 3 )R = C 3V C4 C 2 C 3 V in sr (C C 3 ) - I L3 s(c 2 C 3 ) Michael Tse: HF Filter Design 7

18 3.2 Signal Flow Graph Synthesis (con t) Signal flow graph for state V C2 : R I I 3 I L3 L 3 I 5 V in sr (C 2 C 3 ) V C2 C 3 C 2 C 3 V C4 V in V C2 I C3 C 2 C 3 C 4 V C4 R 5 V out - s(c 2 C 3 ) sr (C 2 C 3 ) OR V in V C2 C 3 C 2 C 3 V C4 I L3 sr (C 2 C 3 ) Cobining siilar factors together R I L3 Michael Tse: HF Filter Design 8

19 3.2 Signal Flow Graph Synthesis (con t) State V C4 : I L3 L 3 sc 4 V C 4 V out R 5 = I L3 sc 3 (V C 2 -V C4 ) s(c 4 C 3 )V C 4 = -V out R 5 I L3 sc 3 V C 2 V in R I V C2 I 3 I C3 C 2 C C 3 4 I 5 V C4 R 5 V out V C4 = -V out sr 5 (C 3 C 4 ) I L3 s(c 3 C 4 ) C 3V C 2 C 3 C 4 V C2 C 3 C 3 C 4 V C4 V out V C2 C 3 C 3 C 4 V C4 V out s(c 3 C 4 ) I L3 sr 5 (C 3 C 4 ) R 5 I L3 sr 5 (C 3 C 4 ) Michael Tse: HF Filter Design 9

20 3.2 Signal Flow Graph Synthesis (con t) State I L3 : I L3 L 3 sl 3 I L3 = V C 2 -V C4 R I I 3 I 5 I L3 = V C2 -V C 4 sl 3 V in V C2 I C3 C 2 C 3 C 4 V C4 R 5 V out V C2 V C4 sl 3 I L3 Michael Tse: HF Filter Design 20

21 3.2 Signal Flow Graph Synthesis (con t) Cobining the three sub-graph, we get the final signal flow graph: C 3 V in R I V C2 I L L3 3 I 3 I C3 C 2 C C 3 4 I 5 V C4 R 5 V out C 2 C 3 V in V C2 C 3 C 4 C 3 V C4 V out sr (C 2 C 3 ) R sl 3 sr (C 3 C 4 ) R I L3 R = R 5 Michael Tse: HF Filter Design 2

22 3.2 Signal Flow Graph Synthesis (con t) We can now synthesize the circuit with g-c. The rules are:. The branch is g. 2. All transconductances are /R. 3. /s branch is cap to ground. 4. Gains C 3 /(C 2 C 3 ) and C 3 /(C 4 C 3 ) can be realized by capacitor ladder. V C2 C 2 C 3 C 4 V C4 g C 3 g V in g V C2 g g g g C L3 V C4 C 2 C 4 V out Exercise: Convert it to a balanced g-c circuit. Michael Tse: HF Filter Design 22

23 4. REALISATION OF TRANSCONDUCTORS Transconductors (g blocks) can be realized in BJT for or MOSFET for. Bipolar:. Fixed transconductor cascaded with gain cell. A fixed transconductor is usually a differential pair linearized by resistor degeneration. 2. Differential input stage with ultiple inputs, with transistor scaling for better linearity. MOS:. Fixed-bias triode MOS transistor as resistor. Multiple outputs are possible using irrors. 2. Varying-bias triode MOS transistor as resistor. 3. Differential input with constant drain-source current. To avoid confusion, in the next pages, we use G to stand for the transconductance of the whole block, and g for the transistor s. Michael Tse: HF Filter Design 23

24 4. BJT Transconductors Fixed transconductance using resistor I I I I V i i o i o Q Q 2 R E /2 R E /2 2I V i i o R E i o Q Q 2 I I No bias current flows in R E. The CM voltage is nearly zero, hence larger CM range. (The base of each side ust not be less than Vi/2, or the transistor will be cut off.) i o V i = G = 2 R E g Note: Distortion due to non-constant G. So, linearity can be iproved if R E is uch greater than /g of the transistor. Moreover, if V be is assued fixed, V i appears purely across resistor and hence G = /R E (independent of g ). Michael Tse: HF Filter Design 24

25 4. BJT Transconductors (con t) Finding the G for this fixed transconductance Half-circuit equivalent odel: V i I i o i o Q Q 2 R E /2 R E /2 2I I V i 2 i o = g V i 2 v be r π g v be Ê Á Á Á Ë r p r p b R E 2 R E /2 ˆ Ê Á = V i Á Á Ë 2 g R E i o ˆ i o V i = G = 2 R E g Michael Tse: HF Filter Design 25

26 4. BJT Transconductors (con t) Gain-cell transconductor (tunable G ) V i Q Q 3 4 Q Q 2 R E level shifter V LS I 2 I 2 V LS Q 5 Q 6 i o i o Ê G = Á Ë R E ˆ Ê I ˆ 2 Á Ë I The transconductance can be tuned by setting the current ratio I 2 /I. 2I 2 I I Michael Tse: HF Filter Design 26

27 4.2 MOSFET Transconductors Fixed-bias triode MOSFET using a MOSFET operating in triode region to siulate a resistor I I MOSFET Q 9 in triode region acting as resistor I i o Q 5 Q V Q 2 i V i Q 6 V c G = I i o Transconductance is i o V i -V i = C ox Ê Á Ë W L ˆ 9 ( v gs9 -V TH ) Q 9 Q 7 Q 3 Q 4 Q 8 I 2 I 2 This G can be easily odified to give ultiple outputs! (using irrors) Michael Tse: HF Filter Design 27

28 4.2 MOSFET Transconductors (con t) Varying bias triode MOSFET iproved linearity I I i o Q Q 2 V Q 3 i o Q3 and Q4 are in triode region and undergo varying bias conditions (because their gates are not connected to fixed bias.) Why is linearity iproved? Try the exercise on next page. Transconductance is V 2 Q 4 I I G = i o V -V 2 = where k n = C ox 2 4k k 3 I ( k 4k 3 ) k Ê W ˆ Á Ë L n Michael Tse: HF Filter Design 28

29 EXERCISE Consider the circuit of the previous page. Suppose I = 00µA, µc ox = 96µA/V2, (W/L) = (W/L) 2 = 20, (W/L) 3 = 3, and V 2 = 0. (a) Assuing a perfectly linear transconductor, find i o when V =2.5V and 250V, using the forula given in the previous page. (b) Assue the gates of Q 3 and Q 4 are connected to ground and use classical odels for both the triode and active regions. Find the true value of i o when V =2.5V and 250V. Copare your results with (c) those found in (a). Repeat (b), assuing the gates of Q 3 and Q 4 are connected to the input signals as shown in the circuit. (d) Coent on the linearity iproveent, if any, when varying bias triode transistor is used. Michael Tse: HF Filter Design 29