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1 ltc1562 very low noise, low distortion active rc quad universal filter features descriptio n u n continuous timeno clock n four 2nd order filter sections, 10khz to 150khz center frequency n 0.5% typical center frequency accuracy n 0.3% typical center frequency accuracy (a grade) n wide variety of response shapes n lowpass, bandpass and highpass responses n 103db typical s/n, 5v supply (q = 1) n 97db typical s/n, single 5v supply (q = 1) n 96db typical s/(n + thd) at 5v supply, 20khz input n rail-to-rail input and output voltages n dc accurate to 3mv (typ) n zero-power shutdown mode n single or dual supply, 5v to 10v total n resistor-programmable f o , q, gain the ltc ? 1562 is a low noise, low distortion continuous-time filter with rail-to-rail inputs and outputs, optimized for a center frequency (f o ) of 10khz to 150khz. unlike most monolithic filters, no clock is needed. four independent 2nd order filter blocks can be cascaded in any combination, such as one 8th order or two 4th order filters. each blocks response is programmed with three external resistors for center frequency, q and gain, using simple design formulas. each 2nd order block provides lowpass and bandpass out- puts. highpass response is available if an external capacitor replaces one of the resistors. allpass, notch and elliptic responses can also be realized. the ltc1562 is designed for applications where dynamic range is important. for example, by cascading 2nd order sections in pairs, the user can configure the ic as a dual 4th order butterworth lowpass filter with 94db signal-to-noise ratio from a single 5v power supply. low level signals can exploit the built-in gain capability of the ltc1562. varying the gain of a section can achieve a dynamic range as high as 118db with a 5v supply. other cutoff frequency ranges can be provided upon request. please contact ltc marketing. frequency (hz) 10k gain (db) 10 0 10 20 30 40 50 60 70 ?0 100k 1m 1562 ta03b amplitude response 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 , 10k r in4 , 10k r in1 10k v in2 v in1 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v ? see typical applications for other cutoff frequencies dc accurate, noninverting, unity-gain, rail-to-rail input and outputs. peak snr ? 100db with 5v supplies v out1 1562 ta01 v out2 r in3 10k ?v 5v r q1 , 5.62k r21, 10k r23, 10k 0.1 f 0.1 f r q3 , 5.62k r24, 10k r q4 , 13k r q2 , 13k r22, 10k typical applicatio n u dual 4th order 100khz butterworth lowpass filter applicatio n s u n high resolution systems (14 bits to 18 bits) n antialiasing/reconstruction filters n data communications, equalizers n dual or i-and-q channels (two matched 4th order filters in one package) n linear phase filtering n replacing lc filter modules , ltc and lt are registered trademarks of linear technology corporation.
2 ltc1562 absolute m axi m u m ratings w ww u package/order i n for m atio n w u u order part number LTC1562CG ltc1562acg ltc1562ig ltc1562aig top view g package 20-lead plastic ssop *g package pins 4, 7, 14, 17 are substrate/shield connections and must be tied to v 1 2 3 4 5 6 7 8 9 10 20 19 18 17 16 15 14 13 12 11 inv b v1 b v2 b v ? v + shdn v ? v2 a v1 a inv a inv c v1 c v2 c v ? v ? agnd v ? v2 d v1 d inv d t jmax = 150 c, q ja = 136 c/w consult factory for military grade parts. electrical characteristics v s = 5v, outputs unloaded, t a = 25 c, shdn pin to logic low, unless otherwise noted. ac specs are for a single 2nd order section, r in = r2 = r q =10k 0.1%, f o = 100khz, unless noted. symbol parameter conditions min typ max units v s total supply voltage 4.75 10.5 v i s supply current v s = 2.375v, r l = 5k, c l = 30pf, outputs at 0v 17.3 19.5 ma v s = 5v, r l = 5k, c l = 30pf, outputs at 0v 19 21.5 ma v s = 2.375v, r l = 5k, c l = 30pf, outputs at 0v l 23.5 ma v s = 5v, r l = 5k, c l = 30pf, outputs at 0v l 25.5 ma output voltage swing v s = 2.375v, r l = 5k, c l = 30pf l 4.0 4.6 v p-p v s = 5v, r l = 5k, c l = 30pf l 9.3 9.8 v p-p v os dc offset magnitude, v2 outputs v s = 2.375v, input at agnd voltage l 315 mv (lowpass response) v s = 5v, input at agnd voltage l 315 mv dc agnd reference point v s = single 5v supply 2.5 v center frequency (f o ) error (note 2) ltc1562 v s = 5v, v2 output has r l = 5k, c l = 30pf 0.5 1.0 % ltc1562a v s = 5v, v2 output has r l = 5k, c l = 30pf 0.3 0.6 % h l lp passband gain (v2 output) v s = 2.375v, f in = 10khz, l 0 + 0.05 + 0.1 db v2 output has r l = 5k, c l = 30pf h b bp passband gain (v1 output) v s = 2.375v, f in = f o , l + 0.2 + 0.5 db v2 output has r l = 5k, c l = 30pf (note 1) total supply voltage (v + to v C ) .............................. 11v maximum input voltage at any pin ....................(v C C 0.3v) v (v + + 0.3v) operating temperature range ltc1562c ................................................ 0 c to 70 c ltc1562i ............................................ C 40 c to 85 c storage temperature range ................. C 65 c to 150 c lead temperature (soldering, 10 sec).................. 300 c
3 ltc1562 symbol parameter conditions min typ max units q error v s = 2.375v, lp output has r l = 5k, c l = 30pf + 3 % wideband output noise, v s = 2.375v, bw = 200khz, input ac gnd 24 m v rms lowpass response (v2 output) v s = 5v, bw = 200khz, input ac gnd 24 m v rms input-referred noise, gain = 100 bw = 200khz, f o = 100khz, q = 1, input ac gnd 4.5 m v rms thd total harmonic distortion, f in = 20khz, 2.8v p-p , v1 and v2 outputs have C 96 db lowpass response (v2 output) r l = 5k, c l = 30pf f in = 100khz, 2.8v p-p , v1 and v2 outputs have C 78 db r l = 5k, c l = 30pf shutdown supply current shdn pin to v + 1.5 15 m a shdn pin to v + , v s = 2.375v 1.0 m a shutdown-input logic threshold 2.5 v shutdown-input bias current shdn pin to 0v C 10 C 20 m a shutdown delay shdn pin steps from 0v to v + 20 m s shutdown recovery delay shdn pin steps from v + to 0v 100 m s inverting input bias current, each biquad 5 pa electrical characteristics v s = 5v, outputs unloaded, t a = 25 c, shdn pin to logic low, unless otherwise noted. ac specs are for a single 2nd order section, r in = r2 = r q =10k 0.1%, f o = 100khz, unless noted. the l denotes specifications that apply over the full operating temperature range. note 1: absolute maximum ratings are those values beyond which the life of a device may be impaired. note 2: f o change from 5v to 2.375 supplies is C 0.15% typical, f o temperature coefficient, C 40 c to 85 c, is 25ppm/ c typical. typical perfor a ce characteristics uw nominal f o (khz) 50 q error (%) 35 30 25 20 15 10 5 0 ? 130 1562 g03 70 90 110 150 120 60 80 100 140 t a = 70 c t a = 25 c r in = r q q = 10 q = 5 q = 2.5 q = 1 q error vs nominal f o (v s = 5v) nominal f o (khz) 50 f o error (%) 0 0.50 1.00 0.75 1.50 1.25 130 1562 g01 0.50 1.00 0.25 0.25 0.75 1.25 1.50 70 90 110 150 120 60 80 100 140 q = 5 q = 2.5 q = 1 f o error vs nominal f o (v s = 5v) nominal f o (khz) 50 f o error (%) 0 0.50 1.00 0.75 1.50 1.25 130 1562 g02 0.50 1.00 0.25 0.25 0.75 1.25 1.50 70 90 110 150 120 60 80 100 140 q = 5 q = 2.5 q = 1 f o error vs nominal f o (v s = 2.5v)
4 ltc1562 typical perfor a ce characteristics uw peak bp gain vs nominal f o (v s = 5v) (figure 3, v1 output) q error vs nominal f o (v s = 2.5v) nominal f o (khz) 50 q error (%) 35 30 25 20 15 10 5 0 ? 130 1562 g04 70 90 110 150 120 60 80 100 140 q = 10 q = 5 q = 2.5 q = 1 t a = 70 c t a = 25 c r in = r q nominal f o (khz) 50 0.5 peak bp gain (db) 0 0.5 1.0 3.0 2.0 70 90 100 140 2.5 1.5 60 80 110 120 130 150 1562 g5 q = 10 q = 5 q = 2.5 q = 1 t a = 70 c t a = 25 c r in = r q nominal f o (khz) 50 0.5 peak bp gain (db) 0 0.5 1.0 3.0 2.0 70 90 100 140 2.5 1.5 60 80 110 120 130 150 1562 g6 q = 10 q = 5 q = 2.5 q = 1 t a = 70 c t a = 25 c r in = r q peak bp gain vs nominal f o (v s = 2.5v) (figure 3, v1 output) distortion vs external load resistance (v s = 5v, 25 c) (figure 8) external load resistance ( w ) 10k ?00 thd (amplitude below fundamental) (db) ?0 ?0 ?0 ?0 ?0 ?0 5k 2k 1562 g09 ?0 ?0 0 ?0 1k f in = 50khz f in = 20khz 2nd order lowpass f o = 100khz q = 0.7 output level 1v rms (2.83v p-p ) 5v supplies lp noise vs nominal f o (v s = 5v, 25 c) (figure 3, v2 output) (r in = r2) nominal f o (khz) 60 10 bp noise ( m v rms ) 15 25 30 35 60 45 80 100 110 1562 g08 20 50 55 40 70 90 120 130 140 q = 5 q = 2.5 q = 1 pi n fu n ctio n s uuu power supply pins: the v + and v C pins should be bypassed with 0.1 m f capacitors to an adequate analog ground or ground plane. these capacitors should be connected as closely as possible to the supply pins. in the 20-lead ssop package, the additional pins 4, 7, 14 and 17 are internally connected to v C (pin 16) and should also be tied to the same point as pin 16 for best shielding. low noise linear supplies are recommended. switching sup- plies are not recommended as they will lower the filter dynamic range. analog ground (agnd): the agnd pin is the midpoint of an internal resistive voltage divider, developing a potential halfway between the v + and v C pins, with an equivalent series resistance nominally 7k w . this serves as an inter- nal ground reference. filter performance will reflect the quality of the analog signal ground and an analog ground plane surrounding the package is recommended. the analog ground plane should be connected to any digital ground at a single point. for dual supply operation, the agnd pin should be connected to the ground plane bp noise vs nominal f o (v s = 5v, 25 c) (figure 3, v1 output) (r in = r q ) nominal f o (khz) 60 10 noise ( v rms ) 15 25 30 35 60 45 80 100 110 1562 g07 20 50 55 40 70 90 120 130 140 q = 5 q = 2.5 q = 1
5 ltc1562 pi n fu n ctio n s uuu shutdown (shdn): when the shdn input goes high or is open-circuited, the ltc1562 enters a zero-power shut- down state and only junction leakage currents flow. the agnd pin and the amplifier outputs (see figure 3) assume a high impedance state and the amplifiers effectively disappear from the circuit. (if an input signal is applied to a complete filter circuit while the ltc1562 is in shutdown, some signal will normally flow to the output through passive components around the inactive op amps.) a small pull-up current source at the shdn input defaults the ltc1562 to the shutdown state if the shdn pin is left floating . therefore, the user must connect the shdn pin to a logic low (0v for 5v supplies, v C for 5v total supply) for normal operation of the ltc1562. (this con- vention permits true zero-power shutdown since not even the driving logic must deliver current while the part is in shutdown.) with a single supply voltage, use v C for logic low do not connect shdn to the agnd pin. (figure 1). for single supply operation, the agnd pin should be bypassed to the ground plane with at least a 0.1 m f capacitor (at least 1 m f for best ac performance) (figure 2). figure 1. dual supply ground plane connection (including substrate pins 4, 7, 14, 17) 0.1 m f v 1562 f01 digital ground plane (if any) v + ltc1562 0.1 m f analog ground plane 20 19 18 17 16 15 14 13 12 11 1 2 3 4 5 6 7 8 9 10 single-point system ground 1 m f 1562 f01 digital ground plane (if any) v + ltc1562 v + /2 reference 0.1 m f analog ground plane 20 19 18 17 16 15 14 13 12 11 1 2 3 4 5 6 7 8 9 10 single-point system ground figure 2. single supply ground plane connection (including substrate pins 4, 7, 14, 17) + + r2 r q v in inv *r1 and c are precision internal components v2 v1 1/4 ltc1562 1562 f01 c 1 sr1c* z in z in type r c response at v1 bandpass highpass response at v2 lowpass bandpass 10k w r2 in each case, q = f o = (100khz) rq r2 () 100khz f o () figure 3. equivalent circuit of a single 2nd order section (inside dashed line) shown in typical connection. form of z in determines response types at the two outputs (see table)
6 ltc1562 pi n fu n ctio n s uuu inv a, inv b, inv c, inv d: each of the inv pins is a virtual- ground summing point for the corresponding 2nd order section. for each section, external components z in , r2, r q connect to the inv pin as shown in figure 3 and described further in the applications information. note that the inv pins are sensitive internal nodes of the filter and will readily receive any unintended signals that are capacitively coupled into them. capacitance to the inv nodes will also affect the frequency response of the filter sections. for these reasons, printed circuit connections to the inv pins must be kept as short as possible, less than one inch (2.5cm) total and surrounded by a ground plane. v1 a, v1 b, v1 c, v1 d: output pins. provide a bandpass, highpass or other response depending on external cir- cuitry (see applications information section). each v1 pin also connects to the r q resistor of the corresponding 2nd order filter section (see figure 3 and applications informa- tion). each output is designed to drive a nominal net load of 5k w and 30pf, which includes the loading due to the external r q . distortion performance improves when the outputs are loaded as lightly as possible. some earlier literature refers to these outputs as bp rather than v1. v2 a, v2 b, v2 c, v2 d: output pins. provide a lowpass, bandpass or other response depending on external cir- cuitry (see applications information section). each v2 pin also connects to the r2 resistor of the corresponding 2nd order filter section (see figure 3 and applications informa- tion). each output is designed to drive a nominal net load of 5k w and 30pf, which includes the loading due to the external r2. distortion performance improves when the outputs are loaded as lightly as possible. some earlier literature refers to these outputs as lp rather than v2. block diagra w overall block diagram showing four 3-terminal 2nd order sections v + v shdn 1562 bd 2nd order sections r r inv v1 v2 c shutdown switch shutdown switch agnd v + v + inv v1 v2 inv v1 v2 inv v1 v2 c cc ab dc + + +
7 ltc1562 applicatio n s i n for m atio n wu u u functional description the ltc1562 contains four matched, 2nd order, 3-termi- nal universal continuous-time filter blocks, each with a virtual-ground input node (inv) and two rail-to-rail out- puts (v1, v2). in the most basic applications, one such block and three external resistors provide 2nd order lowpass and bandpass responses simultaneously (figure 3, with a resistor for z in ). the three external resistors set standard 2nd order filter parameters f o , q and gain. a combination of internal precision components and exter- nal resistor r2 sets the center frequency f o of each 2nd order block. the ltc1562 is trimmed at manufacture so that f o will be 100khz 0.5% if the external resistor r2 is exactly 10k. however, lowpass/bandpass filtering is only one specific application for the 2nd order building blocks in the ltc1562. highpass response results if the external impedance z in in figure 3 becomes a capacitor c in (whose value sets only gain, not critical frequencies) as described below. responses with zeroes are available through other con- nections (see notches and elliptic responses). moreover, the virtual-ground input gives each 2nd order section the built-in capability for analog operations such as gain (preamplification), summing and weighting of multiple inputs, handling input voltages beyond the power supplies or accepting current or charge signals directly. these operational filter tm frequency-selective building blocks are nearly as versatile as operational amplifiers. the user who is not copying exactly one of the typical applications schematics shown later in this data sheet is urged to read carefully the next few sections through at least signal swings, for orientation about the ltc1562, before attempting to design custom application circuits. also available free from ltc, and recommended for de- signing custom filters, is the general-purpose analog filter design software filtercad tm for windows ? . this software includes tools for finding the necessary f 0 , q and gain parameters to meet target filter specifications such as frequency response. setting f o and q each of the four 2nd order sections in the ltc1562 can be programmed for a standard filter function (lowpass, bandpass or highpass) when configured as in figure 3 with a resistor or capacitor for z in . these transfer func- tions all have the same denominator, a complex pole pair with center frequency w o = 2 p f o and quality parameter q. (the numerators depend on the response type as de- scribed below.) external resistors r2 and r q set f o and q as follows: f crr k r khz o == ? ? ? ? () 1 212 10 2 100 p () w q r rr r kr r r khz f qqq o == = ? ? ? ? () ( ) 1 2 10 2 2 100 w r1 = 10k and c = 159pf are internal to the ltc1562 while r2 and r q are external. a typical design procedure proceeds from the desired f o and q as follows, using finite-tolerance fixed resistors. first find the ideal r2 value for the desired f o : r ideal khz f k o 2 100 10 2 () = ? ? ? ? () w then select a practical r2 value from the available finite- tolerance resistors. use the actual r2 value to find the desired r q , which also will be approximated with finite tolerance: rq kr q = () 10 2 w the f o range is approximately 10khz to 150khz, limited mainly by the magnitudes of the external resistors required. as shown above, r2 varies with the inverse square of f o . this relationship desensitizes f o to r2s operational filter and filtercad are trademarks of linear technology corporation. windows is a registered trademark of microsoft corporation.
8 ltc1562 applicatio n s i n for m atio n wu u u tolerance (by a factor of 2 incrementally), but it also implies that r2 has a wider range than f o . (r q and r in also tend to scale with r2.) at high f o these resistors fall below 5k, heavily loading the outputs of the ltc1562 and leading to increased thd and other effects. at the other extreme, a lower f o limit of 10khz reflects an arbitrary upper resistor limit of 1m w . the ltc1562s mos input circuitry can accommodate higher resistor values than this, but junc tion leakage current from the input protection cir- cuitry may cause dc errors. the 2nd order transfer functions h lp (s), h bp (s) and h hp (s) (below) are all inverting so that, for example, at dc the lowpass gain is C h l . if two such sections are cas- caded, these phase inversions cancel. thus, the filter in the application schematic on the first page of this data sheet is a dual dc preserving, noninverting, rail-to-rail lowpass filter, approximating two straight wires with frequency selectivity. figure 4 shows further details of 2nd order lowpass, bandpass and highpass responses. configurations to obtain these responses appear in the next three sections. basic lowpass when z in of figure 3 is a resistor of value r in , a standard 2nd order lowpass transfer function results from v in to v2 (figure 5): vs vs hs h sqs in lp lo oo 2 2 2 2 () () () / == + () + w ww the dc gain magnitude is h l = r2/r in . (note that the transfer function includes a sign inversion.) parameters w o (= 2 p f o ) and q are set by r2 and r q as above. for a 2nd order lowpass response the gain magnitude becomes qh l inv v1 2nd order 1/4 ltc1562 v2 1562 f05 r2 r q r in v in v out f l gain (v/v) 0.707 h b h b f o f (log scale) bandpass response f h gain (v/v) 0.707 h l h p h l h h f p f (log scale) lowpass response f c f c gain (v/v) 0.707 h h h p f p f (log scale) highpass response q f ff fff ff qq ff qq o hl olh l o ho == = + ? ? ? ? + ? ? ? ? ? ? =+ ? ? ? ? + ? ? ? ? ? ? ; 1 2 1 2 1 1 2 1 2 1 2 2 ff qq ff q hh q q co po pl = ? ? ? ? + ? ? ? ? + = = ? ? ? ? ? ? ? ? 1 1 2 1 1 2 1 1 1 2 1 1 1 1 4 22 2 2 2 ff qq ff q hh q q co po ph = ? ? ? ? + ? ? ? ? + ? ? ? ? ? ? = ? ? ? ? = ? ? ? ? ? ? ? ? 1 1 2 1 1 2 1 1 1 2 1 1 1 1 4 22 2 1 2 1 2 figure 4. characteristics of standard 2nd order filter responses figure 5. basic lowpass configuration
9 ltc1562 applicatio n s i n for m atio n wu u u parameters w o = 2 p f o and q are set by r2 and r q as above. the highpass gain parameter is h h = c in /159pf. for a 2nd order highpass response the gain magnitude at frequency f o is qh h , and approaches h h at high frequen- cies (f >> f o ). for q > 0.707, a gain peak occurs at a frequency above f o as shown in figure 4. the transfer function includes a sign inversion. at frequency f o , and for q > 0.707, a gain peak occurs at a frequency below f o , as shown in figure 4. basic bandpass there are two different ways to obtain a bandpass function in figure 3, both of which give the following transfer function form: hs hqs sqs bp bo oo () / / = () + () + w ww 2 2 w o = 2 p f o and q are set by r2 and r q as described previ- ously in setting f o and q. when z in is a resistor of value r in , a bandpass response results at the v1 output (figure 6a) with a gain parameter h b = r q /r in . alternatively, a capacitor of value c in gives a bandpass response at the v2 output (figure 6b), with the same h bp (s) expression, and the gain parameter now h b = (r q /10k w )(c in /159pf). this transfer function has a gain magnitude of h b (its peak value) when the frequency equals f o and has a phase shift of 180 at that frequency. q measures the sharpness of the peak (the ratio of f o to C 3db bandwidth) in a 2nd order bandpass function, as illustrated in figure 4. inv v1 2nd order 1/4 ltc1562 (b) capacitive input (a) resistive input v2 1562 f06 r2 r q c in v in v out inv v1 2nd order 1/4 ltc1562 v2 r2 r q r in v in v out figure 6. basic bandpass configurations basic highpass when z in of figure 3 is a capacitor of value c in , a highpass response appears at the v1 output (figure 7). vs vs hs hs sqs in hp h oo 1 2 2 2 () () () / == + () + ww inv v1 2nd order 1/4 ltc1562 v2 1562 f07 r2 r q c in v in v out figure 7. basic highpass configuration signal swings the v1 and v2 outputs are capable of swinging to within roughly 100mv of each power supply rail. as with any analog filter, the signal swings in each 2nd order section must be scaled so that no output overloads (saturates), even if it is not used as a signal output. (filter literature often calls this the dynamics issue.) when an unused output has a larger swing than the output of interest, the sections gain or input amplitude must be scaled down to avoid overdriving the unused output. the ltc1562 can still be used with high performance in such situations as long as this constraint is followed. for an ltc1562 section as in figure 3, the magnitudes of the two outputs v2 and v1, at a frequency w = 2 p f, have the ratio, |()| |()| () vj vj khz f 2 1 100 w w = regardless of the details of z in . therefore, an input fre- quency above or below 100khz produces larger output amplitude at v1 or v2, respectively. this relationship can guide the choice of filter design for maximum dynamic range in situations (such as bandpass responses) where there is more than one way to achieve the desired fre- quency response with an ltc1562 section.
10 ltc1562 because 2nd order sections with q 3 1 have response peaks near f o , the gain ratio above implies some rules of thumb: f o < 100khz t v2 tends to have the larger swing f o > 100khz t v1 tends to have the larger swing. the following situations are convenient because the relative swing issue does not arise. the unused outputs swing is naturally the smaller of the two in these cases: lowpass response (resistor input, v2 output, figure 5) with f o < 100khz bandpass response (capacitor input, v2 output, figure 6b) with f o < 100khz bandpass response (resistor input, v1 output, figure 6a) with f o > 100khz highpass response (capacitor input, v1 output, figure 7) with f o > 100khz the ltc1562-2, a higher frequency derivative of the ltc1562, has a design center f o of 200khz compared to 100khz in the ltc1562. the rules summarized above apply to the ltc1562-2 but with 200khz replacing the 100khz limits. thus, an ltc1562-2 lowpass filter section with f o below 200khz automatically satisfies the desirable condition of the unused output carrying the smaller signal swing. applicatio n s i n for m atio n wu u u level inputs require further dynamic range, reducing the value of z in boosts the signal gain while reducing the input referred noise. this feature can increase the snr for low level signals. varying or switching z in is also an efficient way to effect automatic gain control (agc). from a system viewpoint, this technique boosts the ratio of maximum signal to minimum noise, for a typical 2nd order lowpass response (q = 1, f o = 100khz), to 118db. input voltages beyond the power supplies properly used, the ltc1562 can accommodate input voltage excursions well beyond its supply voltage. this requires care in design but can be useful, for example, when large out-of-band interference is to be removed from a smaller desired signal. the flexibility for different input voltages arises because the inv inputs are at virtual ground potential, like the inverting input of an op amp with negative feedback. the ltc1562 fundamentally responds to input current and the external voltage v in appears only across the external impedance z in in figure 3. to accept beyond-the-supply input voltages, it is impor- tant to keep the ltc1562 powered on, not in shutdown mode, and to avoid saturating the v1 or v2 output of the 2nd order section that receives the input. if any of these conditions is violated, the inv input will depart from a virtual ground, leading to an overload condition whose recovery timing depends on circuit details. in the event that this overload drives the inv input beyond the supply voltages, the ltc1562 could be damaged. the most subtle part of preventing overload is to consider the possible input signals or spectra and take care that none of them can drive either v1 or v2 to the supply limits. note that neither output can be allowed to saturate, even if it is not used as the signal output. if necessary the passband gain can be reduced (by increasing the imped- ance of z in in figure 3) to reduce output swings. the final issue to be addressed with beyond-the-supply inputs is current and voltage limits. current entering the virtual ground inv input flows eventually through the output circuitry that drives v1 and v2. the input current magnitude ( ? v in ? / ? z in ? in figure 3) should be limited by design to less than 1ma for good distortion performance. on the other hand, the input voltage v in appears across the low level or wide range input signals the ltc1562 contains a built-in capability for low noise amplification of low level signals. the z in impedance in each 2nd order section controls the blocks gain. when set for unity passband gain, a 2nd order section can deliver an output signal more than 100db above the noise level. if low figure 8. 100khz, q = 0.7 lowpass circuit for distortion vs loading test inv v1 2nd order 1/4 ltc1562 v2 1562 f08 r2 10k c l 30pf r l (external load resistance) r q 6.98k r in 10k v in v out
11 ltc1562 applicatio n s i n for m atio n wu u u external component z in , usually a resistor or capacitor. this component must of course be rated to sustain the magnitude of voltage imposed on it. lowpass t input circuit the virtual ground inv input in the operational filter block provides a means for adding an extra lowpass pole to any resistor-input application (such as the basic lowpass, figure 5, or bandpass, figure 6a). the resistor that would otherwise form z in is split into two parts and a capacitor to ground added, forming an r-c-r t network (figure 9). this adds an extra, independent real pole at a fre- quency: f rc p pt = p 1 2 where c t is the new external capacitor and r p is the parallel combination of the two input resistors r ina and r inb . this pair of resistors must normally have a pre- scribed series total value r in to set the filters gain as described above. the parallel value r p can however be set arbitrarily (to r in /4 or less) which allows choosing a convenient standard capacitor value for c t and fine tuning the new pole with r p . inv v1 2nd order 1/4 ltc1562 v2 1562 f09 r2 r q r inb r ina c t v in figure 9. lowpass t input circuit the procedure therefore is to begin with the target extra pole frequency f p . determine the series value r in from the gain requirement. select a capacitor value c t such that r p = 1/(2 p f p c t ) is no greater than r in /4, and then choose r ina and r inb that will simultaneously have the parallel value r p and the series value r in . such r ina and r inb can be found directly from the expression: 1 2 1 2 4 2 rrrr in in in p () a practical limitation of this technique is that the c t capaci- tor values that tend to be required (hundreds or thousands of pf) can destabilize the op amp in figure 3 if r inb is too small, leading to ac errors such as q enhancement. for this reason, when r ina and r in b are unequal, preferably the larger of the two should be placed in the r inb position. highpass t input circuit a method similar to the preceding technique adds an extra highpass pole to any capacitor-input application (such as the bandpass of figure 6b or the highpass of figure 7). this method splits the input capacitance c in into two series parts c ina and c inb , with a resistor r t to ground between them (figure 10). this adds an extra 1st order highpass corner with a zero at dc and a pole at the frequency: f rc p tp = p 1 2 where c p = c ina + c inb is the parallel combination of the two capacitors. at the same time, the total series capaci- tance c in will control the filters gain parameter (h h in basic highpass). for a given series value c in , the parallel value c p can still be set arbitrarily (to 4c in or greater). figure 10. highpass t input circuit inv v1 2nd order 1/4 ltc1562 v2 1562 f10 r2 r q c inb r t v in c ina the procedure then is to begin with the target corner (pole) frequency f p . determine the series value c in from the gain requirement (for example, c in = h h (159pf) for a highpass). select a resistor value r t such that c p = 1/(2 p r t f p ) is at least 4c in , and select c ina and c inb that will simultaneously have the parallel value c p and the series value c in . such c ina and c inb can be found directly from the expression: 1 2 1 2 4 2 cccc p p in p ()
12 ltc1562 applicatio n s i n for m atio n wu u u C 3db frequencies f l and f h are widely separated from this peak. the ltc1562s f o is trimmed in production to give an accurate 180 phase shift in the configuration of figure 6a with resistor values setting f 0 = 100khz and q = 1. table 1 below shows typical differences between f o values measured via the bandpass 180 criterion and f o values measured using the two other methods listed above (figure 6a, r in = r q ). table 1 f o q = 1 q = 1 q = 5 q = 5 (bp 180 ) bp-peak f o ?| l | h f o bp-peak f o ?| l | h f o 60khz + 0.3% + 0.3% + 0.05% + 0.05% 100khz + 0.6% + 0.6% + 0.1% + 0.1% 140khz + 0.8% + 0.8% + 0.15% + 0.15% ltc1562 demo board the ltc1562 demo board is assembled with an ltc1562 or ltc1562a in a 20-pin ssop package and power supply decoupling capacitors. jumpers on the board configure the ltc1562 for dual or single supply operation and power shutdown. pads for surface mount resistors and capaci- tors are provided to build application-specific filters. also provided are terminals for inputs, outputs and power supplies. this procedure can be iterated, adjusting the value of r t , to find convenient values for c ina and c inb since resistor values are generally available in finer increments than capacitor values. different f o measures standard 2nd order filter algebra, as in figure 4 and the various transfer-function expressions in this data sheet, uses a center frequency parameter f o (or w o , which is 2 p f o ). f o can also be measured in practical ways, includ- ing: ? the frequency where a bandpass response has 180 phase shift ? the frequency where a bandpass response has peak gain ? the geometric mean of the C 3.01db gain frequencies in a bandpass ( ?| l | h in figure 4) an ideal mathematical 2nd order response yields exactly the same frequency by these three measures. however, real 2nd order filters with finite-bandwidth circuitry show small differences between the practical f o measures, which may be important in critical applications. the issue is chiefly of concern in high-q bandpass applications where, as the data below illustrate, the different f 0 mea- surements tend to converge anyway for the ltc1562. at low q the bandpass peak is not sharply defined and the
13 ltc1562 typical applicatio n s u (basic) quad 3rd order butterworth lowpass filter, gain = C 1 quad 3rd order butterworth f C 3db f C 3db f C 3db f C 3db f C 3db f C 3db f C 3db lowpass filters 20khz 40khz 60khz 80khz 100khz 120khz 140khz c in 220pf 1000pf 1000pf 1000pf 1000pf 1000pf 1000pf r ina 44.2k 4.32k 3.16k 2.43k 1.96k 1.87k 1.69k r inb 205k 57.6k 24.3k 13.0k 8.06k 5.11k 3.4k r q 249k 61.9k 27.4k 15.4k 10.0k 6.98k 5.11k r2 249k 61.9k 27.4k 15.4k 10.0k 6.98k 5.11k all four sections have identical r ina , r inb and c in values. all resistor values are 1% frequency (hz) 10k gain (db) 10 0 10 20 30 40 50 ?0 100k 1m 1562 ta05b f 3db = 100khz 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in1b r in1a r in3a v in1 v in3 c in1 v in2 1562 ta05a v out2 v out3 v out4 v out1 r in3b ?v 5v r q1 r21 r23 0.1 f 0.1 f r q3 r24 r q4 r q2 r22 c in2 c in3 r in2b r in2a v in4 c in4 r in4b r in4a schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v amplitude response
14 ltc1562 typical applicatio n s u (basic) 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 r in4 r in1 v in2 v in1 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v v out1 1562 ta03a v out2 r in3 ?v 5v r q1 r21 r23 0.1 f 0.1 f r q3 r24 r q4 r q2 r22 dual 4th order lowpass filters amplitude response frequency (hz) 10k gain (db) 10 0 10 20 30 40 50 60 70 ?0 100k 1m 1562 ta03b butterworth f 3db = 100khz 10k r21, r23, r in1 , r in3 = quick design formulas for some popular response types: 2 100khz | c butterworth (maximally flat passband) for f c 10khz to 140khz 14.24k 2 100khz | c chebyshev (equiripple passband) for f c 20khz to 120khz 3.951k 2 100khz | c bessel (good transient response) for f c 10khz to 70khz 5.412k r q1 , r q3 = 100khz | c 7.26k 100khz | c 5.066k 100khz | c 10k r22, r24, r in2 , r in4 = 2 100khz | c 7.097k 2 100khz | c 4.966k 2 100khz | c 13.07k r q2 , r q4 = notes: f c is the cutoff frequency: for butterworth and bessel, response is 3db down at f c . for chebyshev filters with 0.1db passband ripple up to 0.95 f c , use ltc1562 ??grade. example: butterworth response, f c = 50khz. from the formulas above, r21 = r23 = r in1 = r in3 = 10k(100khz/50khz) 2 = 40k. r q1 = r q3 = 5.412k(100khz/50khz) = 10.82k. r22 = r24 = r in2 = r in4 = 10k(100khz/50khz) 2 = 40k. r q2 = r q4 = 13.07k(100khz/50khz) = 26.14k. use nearest 1% values. 100khz | c 17.53k 100khz | c 3.679k 100khz | c 1562 ta03 table
15 ltc1562 typical applicatio n s u (basic) 8th order lowpass filters amplitude response r21 = r in1 = 10k quick design formulas for some popular response types: 2 100khz | c butterworth (maximally flat passband) for f c 10khz to 140khz r21 = 7.51k , r in1 = 2.2r21* , r in4 = 2 100khz | c chebyshev (equiripple passband) for f c 20khz to 120khz bessel (good transient response) for f c 10khz to 70khz r q1 = 6.01k 100khz | c r q1 = 119.3k 100khz | c 100khz | c + 560khz 100khz | c + 530khz r24* 2.2 100khz | c + 2440khz r22 = r in2 = 10k 2 100khz | c r22 = r in2 = 14.99k 2 100khz | c r q2 = 9k notes: f c is the cutoff frequency: for butterworth and bessel, response is 3db down at f c . for chebyshev filters with 0.1db passband ripple up to 0.95 f c , use ltc1562 ??grade. *the resistor values marked with an asterisk (*) in the chebyshev formulas (r21 and r24) should be rounded to the nearest standard finite-tolerance value before computing the values dependent on them (r in1 and r in4 respectively). example: chebyshev response, f c = 100khz. the formulas above give r21 = 7.51k, nearest standard 1% value 7.50k. using this 1% value gives r in1 = 16.5k, already a standard 1% value. r q1 = 18.075k, nearest 1% value 18.2k. r22 = r in2 = 14.99k, nearest 1% value 15k. r q2 = 11.02k, nearest 1% value 11k. r23 = r in3 = 7.15k, already a standard 1% value. r q3 = 18.75k, nearest 1% value 18.7k. r24 = 26.7k, already a standard 1% value. this gives r in4 = 12.14k, nearest 1% value 12.1k. r q4 = 8.75k, nearest 1% value 8.66k. 100khz | c r q2 = 279.9k 100khz | c r23 = r in3 = 10k 2 100khz | c r23 = r in3 = 7.15k 2 100khz | c r q3 = 5.1k 100khz | c r q3 = 118.1k 100khz | c r24 = r in4 = 10k 2 100khz | c r24 = 26.7k 2 100khz | c r q4 = 25.63k 100khz | c r21 = r in1 = 2.61k 2 100khz | c r q1 = 3.63k 100khz | c r22 = r in2 = 2.07k 2 100khz | c r q2 = 5.58k 100khz | c r23 = r in3 = 2.96k 2 100khz | c r q3 = 3.05k 100khz | c r24 = r in4 = 3.14k 2 100khz | c r q4 = 2.84k 100khz | c r q4 = 8.75k 100khz | c 1562 ta04 table 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 r in4 r in1 v in v out 1562 ta04a r in3 ?v 5v r q1 r21 r23 0.1 f 0.1 f r q3 r24 r q4 r q2 r22 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v frequency (hz) gain (db) 10 0 10 20 30 40 50 60 70 80 ?0 10k 100k 500k 1562 ta04b chebyshev f c = 100khz
16 ltc1562 (basic) typical applicatio n s u amplitude response 8th order bandpass filter, single 5v supply, C 3db bandwidth = center frequency 10 r21 = r23 = 10.6k quick design formulas for center frequency f c (recommended range 40khz to 140khz): 2 100khz | c r q1 = r q3 = 164.6k 100khz | c 100khz | c + 319khz r q2 = r q4 = 143.2k r in2 = r in4 = 100khz | c + 294khz 100khz | c + 286khz r22 = r24 = 9.7k 100khz | c 100khz | c c in1 = c in3 = 159pf 2 10k r q1 r22r q1 c in1 (10k)(10.6pf) notes: r q1 , r22 and c in1 should be rounded to the nearest standard finite-tolerance value before using these values in the later formulas. example: center frequency f c of 80khz. the formulas give r21 = r23 = 16.56k, nearest standard 1% value 16.5k. r q1 = r q3 = 51.56k, nearest 1% value 51.1k. r22 = r24 = 15.15k, nearest 1% value 15k. r q2 = r q4 = 47.86k, nearest 1% value 47.5k. c in1 = c in2 = 31.11pf using 51.1k for r q1 , nearest standard 5% capacitor value 33pf. this and the 1% value r22 = 15k also go into the calculation for r in2 = r in4 = 65.20k, nearest 1% value 64.9k. 1562 ta07 table 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 r in4 v in v out 1562 ta07a 5v r q1 r21 r23 0.1 f 1 f r q3 c in3 c in1 r24 r q4 r q2 r22 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v frequency (khz) 40 gain (db) ?0 ?0 10 104 1562 ta07b ?0 ?0 ?0 ?0 0 ?0 ?0 ?0 56 72 88 48 112 64 80 96 120 f center = 80khz
17 ltc1562 (basic) typical applicatio n s u amplitude response 8th order bandpass filter, single 5v supply, C 1db bandwidth = center frequency 10 frequency (khz) 60 gain (db) ?0 ?0 10 124 1562 ta06b ?0 ?0 ?0 ?0 0 ?0 ?0 ?0 76 92 108 68 132 84 100 116 140 f center = 100khz r21 = r23 = 11.7k quick design formulas for a center frequency f c (recommended range 50khz to 120khz): 2 2 100khz | c r in1 = r in3 = r21 2.56 r22 = r24 = 8.66k 100khz | c | c + 1736khz 100khz r in2 = r in4 = r q2 14.36 | c + 634khz 100khz notes: r21 and r q2 should be rounded to the nearest standard finite-tolerance value before using these values in the later formulas. for f c < 100khz, the maximum peak-to-peak passband input level is (f c /100khz)5v. use ltc1562a for minimum variation of passband gain. example: center frequency f c of 100khz. the formulas give r21 = r23 = 11.7k, nearest standard 1% value 11.5k. this value gives r in1 = r in3 = 82.46k, nearest 1% value 82.5k. r q1 = r q3 = 65.5k, nearest 1% value 64.9k. r22 = r24 = 8.66k, already a standard 1% value. this gives r in2 = r in4 = 32.4k (again already a standard 1% value). r q2 = r q4 = 63.45k, nearest 1% value 63.4k. if ltc1562a is used, resistor tolerances tighter than 1% will further improve the passband gain accuracy. r q1 = r q3 = 215.5k 100khz | c 100khz | c 1562 ta06 table 100khz | c + 229khz r q2 = r q4 = 286.2k 100khz | c + 351khz 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 r in4 r in1 v in v out 1562 ta06a r in3 5v r q1 r21 r23 0.1 f 1 f r q3 r24 r q4 r q2 r22 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v
18 ltc1562 (basic) 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 r in4 r in1 v in v out 1562 ta08a r in3 v v + r q1 r21 r23 0.1 f 0.1 f r q3 r24 r q4 r q2 r22 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v frequency (khz) 40 gain (db) ?0 10 30 120 1562 ta08b ?0 ?0 ?0 0 20 ?0 ?0 ?0 60 80 100 140 160 180 f center = 100khz amplitude response 8th order bandpass filter C 3db bw = f center , gain = 10 f center f center f center f center f center f center f center 10 80khz 90khz 100khz 110khz 120khz 130khz 140khz side b r in1 4.64k 5.23k 6.34k 5.11k 5.11k 5.49k 5.62k r q1 46.4k 52.3k 42.2k 38.3k 34.8k 32.4k 30.1k r21 12.4k 15.4k 10.0k 8.25k 6.98k 5.9k 5.11k sides a, c, d r in2 , r in3 , r in4 46.4k 52.3k 42.2k 38.3k 34.8k 32.4k 30.1k r q2 , r q3 , r q4 46.4k 52.3k 42.2k 38.3k 34.8k 32.4k 30.1k r22, r23, r24 12.4k 15.4k 10.0k 8.25k 6.98k 5.90k 5.11k all resistor values are 1% typical applicatio n s u 8th order bandpass (high frequency) filter C 3db bandwidth = center frequency , gain = 10 10
19 ltc1562 (basic) typical applicatio n s u amplitude response 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 , 5.23k r in4 , 3.4k c in1 150pf v in v out 1562 ta11a r in3 , 8.06k 5v ?v r q1 , 30.1k r21, 110k r23, 5.23k 0.1 f 0.1 f r q3 , 14k r24, 5.23k r q4 , 3.74k r q2 , 5.11k r22, 5.23k schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v ? all resistors = 1% metal film 2nd order 30khz highpass cascaded with 6th order 138khz lowpass 8th order wideband bandpass filter f center = 50khz, C 3db bw 40khz to 60khz 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 c in1 22pf v in v out 1562 ta09a v + v r q1 59k r21 56.2k r in2 69.8k r23 63.4k 0.1 f 1 f r q3 82.5k r24 28.7k r q4 100k r q2 48.7k r22 34.8k c in4 47pf c in3 27pf schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v frequency (khz) ?0 ?0 ?0 ?0 10 0 ?0 ?0 1562 ta09b gain (db) 20 100 amplitude response frequency (khz) 10 gain (db) 20 10 0 10 20 30 40 50 60 70 ?0 100 400 1562 ta11b 8th order highpass 0.05db ripple chebyshev filter f cutoff = 30khz 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 c in1 150pf c in 1562 ta10a v out ?v 5v r q1 , 10.2k r21, 35.7k r23, 107k 0.1 f 0.1 f r q3 , 54.9k r24, 127k r q4 , 98.9k r q2 , 22.1k r22, 66.5k c in3 150pf c in4 150pf c in2 150pf schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v ? total output noise = 40 m v rms amplitude response frequency (hz) 1k gain (db) 10 0 10 20 30 40 50 60 70 80 ?0 10k 100k 1m 1562 ta10b
20 ltc1562 applicatio n s i n for m atio n wu u u notches and elliptic responses the basic (essentially all-pole) ltc1562 circuit tech- niques described so far will serve many applications. however, the sharpest-cutoff lowpass, highpass and bandpass filters include notches (imaginary zero pairs) in the stopbands. a notch, or band-reject, filter has zero gain at a frequency f n . notches are also occasionally used by themselves to reject a narrow band of frequencies. a number of circuit methods will give notch responses from an operational filter block. each method exhibits an input- output transfer function that is a standard 2nd order band- reject response: hs hs sqs br nn oo () / = + ? ? ? + () + 22 22 w ww with parameters w n = 2 p f n and h n set by component values as described below. ( w 0 = 2 p f 0 and q are set for the operational filter block by its r2 and r q resistors as described earlier in setting f 0 and q). characteristically, the gain magnitude |h br (j2 p f)| has the value h n (f n 2 /f 0 2 ) at dc (f = 0) and h n at high frequencies (f >> f n ), so in addition to the notch, the gain changes by a factor: high frequency gain dc gain o n = | | 2 2 the common principle in the following circuit methods is to add a signal to a filtered replica of itself having equal gain and 180 phase difference at the desired notch frequency f n . the two signals then cancel out at frequency f n . the notch depth (the completeness of cancellation) will be infinite to the extent that the two paths have matching gains. three practical circuit methods are presented here, with different features and advantages. examples and design procedures for practical filters using these techniques appear in a series of articles 1 attached to this data sheet on the linear technology web site (www.linear-tech.com). also available free is the analog filter design software, filtercad for windows, recom- mended for designing filters not shown in the typical applications schematics in this data sheet. elementary feedforward notches a textbook method to get a 180 phase difference at frequency f n for a notch is to dedicate a bandpass 2nd order section (described earlier under basic bandpass), which gives 180 phase shift at the sections center frequency f o (figure 11, with c in1 = 0), so that f n = f o . the bandpass section of figure 6a, at its center frequency f o , has a phase shift of 180 and a gain magnitude of h b = r q /r in . a notch results in figure 11 if the paths summed into virtual ground have the same gains at the 180 frequency (then i o = 0). this requires a constraint on the resistor values: r r r r in ff q in 2 2 1 1 = 1 nello sevastopoulos, et al. how to design high order filters with stopband notches using the ltc1562 quad operational filter. attached to this data sheet, available on the ltc web site (www.linear-tech.com). inv v1 2nd order 1/4 ltc1562 v2 r21 r q1 r in1 r in2 r gain i o r ff2 c in1 v in v out 1562 f11 virtual ground + figure 11. feedforward notch configuration for f n 3 f o
21 ltc1562 applicatio n s i n for m atio n wu u u note that the depth of the notch depends on the accuracy of this resistor ratioing. the virtual-ground summing point in figure 11 may be from an op amp as shown, or in a practical cascaded filter, the inv input of another opera- tional filter block. the transfer function in figure 11 with c in1 = 0 is a pure notch (f n = f 0 ) of the h br (s) form above, and the parameters are: |=| = no n gain ff h r r 2 because f n = f 0 in this case, the gain magnitude both at dc and at high frequencies (f >> f n ) is the same, h n (assuming that the op amp in figure 11 adds no significant frequency response). figure 12 shows this. such a notch is ineffi- cient as a cascaded part of a highpass, lowpass or bandpass filter (the most common uses for notches). variations of figure 11 can add a highpass or lowpass shape to the notch, without using more operational filter blocks. the key to doing so is to decouple the notch frequency f n from the center frequency f 0 of the operational filter (this is shown in figures 13 and 15). the next two sections summarize two variations of figure 11 with this highpass/ lowpass shaping, and the remaining section shows a different approach to building notches. feedforward notches for f n > f 0 when c in1 1 0 in figure 11, the notch frequency f n is above the center frequency f 0 and the response has a lowpass shape as well as a notch (figure 13). c in1 contributes phase lead, which increases the notch frequency above the center frequency of the 2nd order operational filter section. the resistor constraint from the previous section also applies here and the h br (s) parameters become: |=| = ? ? ? ? | | ? ? ? ? no in in q n gain ff o n rc rc h r r 1 1 11 1 2 2 2 c is the internal capacitor value in the operational filter (in the ltc1562, 159pf). the configuration of figure 11 is most useful for a stopband notch in a lowpass filter or as an upper stopband notch in a bandpass filter, since the two resistors r in2 and r ff2 can replace the input resistor r in of either a lowpass section (figure 5) or a resistor-input bandpass section (figure 6a) built from a second operational filter. the configuration is figure 12. notch response with f n = f o frequency (khz) 10 ?0 gain (db) ?0 ?0 20 100 1000 1562 f13 0 f o = 100khz f n = 200khz q = 1 dc gain = 0db f n 2 f o 2 dc gain = h n () high freq gain = h n frequency (khz) 10 100 gain (db) ?0 ?0 0 100 1000 an54 ?ta18 ?0 ?0 f n = f o = 100khz h n = 1 q = 1 figure 13. notch response with f n > f o
22 ltc1562 applicatio n s i n for m atio n wu u u robust against tolerances in the c in1 value when f n ap- proaches f 0 (for f n /f 0 1.4, as a rule of thumb) which is attractive in narrow transition-band filters, because of the relative cost of high accuracy capacitors. further applica- tion details appear in part 1 of the series of articles. 1 feedforward notches for f n < f 0 just as feedforward around an inverting bandpass section yields a notch at the sections f 0 (figure 11 with c in1 = 0), feedforward around an inverting lowpass section causes a notch at zero frequency (which is to say, a highpass response). moreover, and this is what makes it useful, introducing a capacitor for phase lead moves the notch frequency up from dc, exactly as c in1 in figure 11 moves the notch frequency up from the center frequency f 0 . in figure 14, the inverting lowpass output (v2) of the opera- tional filter is summed, at a virtual ground, with a fed- forward input signal. capacitor c in1 shifts the resulting notch frequency, f n , up from zero, giving a low frequency notch with a highpass shape (figure 15). the h br (s) response parameters are now: |=| ? ? ? ? ? ? ? ? ? ? ? ? = no qinin n gain ff r r c c r r h r r 1 121 111 2 the constraint required for exact cancellation of the two paths (i.e., for infinite notch depth) becomes: r r rc rc in ff qin 2 2 11 1 = r1 and c are the internal precision components (in the ltc1562, 10k and 159pf respectively) as described above in setting f 0 and q. the configuration of figure 14 is most useful as a lower stopband notch in a bandpass filter, because the resistors r in2 and r ff2 can replace the input resistor r in of a bandpass section made from a second operational filter, as in figure 6a. the configuration is robust against toler- ances in the c in1 value when f n approaches f 0 (for f 0 /f n 1.4, as a rule of thumb) which is attractive in narrow transition-band filters, because of the relative cost of high accuracy capacitors. further application details appear in part 2 of the series of articles. 1 frequency (hz) 10k ?0 gain (db) ?0 ?0 20 100k 1m 1562 f15 0 f o = 100khz f n = 50khz q = 1 high freq gain = 0db f n 2 f o 2 dc gain = h n () high freq gain = h n figure 15. notch response with f n < f 0 figure 14. feedforward notch configuration for f n < f o inv v1 2nd order 1/4 ltc1562 v2 r21 r q1 r in1 r in2 r gain i o r ff2 c in1 v in v out 1562 f14 virtual ground +
23 ltc1562 r-c universal notches a different way to get 180 phase shift for a notch is to use the built-in 90 phase difference between the two opera- tional filter outputs along with a further 90 from an external capacitor. this method achieves deep notches independent of component matching, unlike the previous techniques, and it is convenient for cascaded highpass as well as lowpass and bandpass filters. the v2 output of an operational filter is a time-integrated version of v1 (see figure 3), and therefore lags v1 by 90 over a wide range of frequencies. in figure 16, a notch response occurs when a 2nd order section drives a virtual- ground input through two paths, one through a capacitor and one through a resistor. again, the virtual ground may come from an op amp as shown, or from another opera- tional filters inv input. capacitor c n adds a further 90 to the 90 difference between v1 and v2, producing a wideband 180 phase difference, but frequency-depen- dent amplitude ratio, between currents i r and i c . at the frequency where i r and i c have equal magnitude, i o becomes zero and a notch occurs. this gives a net transfer function from v in to v out in the form of h br (s) as above, with parameters: |= p = ? ? ? ? ? ? ? ? n nn n gain in n rcrc h r r c c 1 21 1 applicatio n s i n for m atio n wu u u dc gain r r r r high frequency gain dc gain rc rc gain in n o n nn = ? ? ? ? ? ? ? ? | | == 1 2 2 21 21 r1 and c are the internal precision components (in the ltc1562, 10k and 159pf respectively) as described above in setting f 0 and q. unlike the notch methods of figures 11 and 14, notch depth from figure 16 is inherent, not derived from compo- nent matching. errors in the r n or c n values alter the notch frequency, f n , rather than the degree of cancellation at f n . also, the notch frequency, f n , is independent of the sections center frequency f 0 , so f n can freely be equal to, higher than or lower than f 0 (figures 12, 13 or 15, respectively) without changing the configuration. the chief drawback of figure 16 compared to the previous methods is a very practical onethe c n capacitor value directly scales h n (and therefore the high frequency gain). capacitor values are generally not available in increments or tolerances as fine as those of resistors, and this configuration lacks the property of the previous two configurations that sensitiv- ity to the capacitor value falls as f n approaches f 0 . figure 16. the r-c universal notch configuration for an operational filter block inv v1 2nd order 1/4 ltc1562 v2 r21 r q1 r in1 r n r gain i o c n v in v out 1562 f16 virtual ground + i r i c
24 ltc1562 typical applicatio n s u (advanced) r q1 30.1k r q3 34k r in3 31.6k r in1 48.7k v in r q2 13k r in2 37.4k r in4 32.4k c in2 24pf r q4 11.5k r22 57.6k r24 32.4k 0.1 f v out ?v 5v r21 31.6k r23 31.6k ltc1562 invb v1b v2b v + shdn v2a v1a inva 20 19 18 16 15 13 12 11 invc v1c v2c v agnd v2d v1d invd 1 2 3 5 6 8 9 10 0.1 f c in4 10pf 1562 ta12a c in3 18pf schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v 8th order 50khz lowpass elliptic filter with 100db stopband attenuation 8th order 100khz elliptic bandpass filter r q1 86.6k r q3 71.5k r in3 294k c in3 18pf r in1 95.3k c in1 5.6pf v in r q2 84.5k r in2 93.1k r ff2 301k r in4 95.3k r ff4 332k r q4 82.5k r22 10k r24 9.53k 0.1 f v out ?v 5v r21 10.7k r23 10k ltc1562 invb v1b v2b v + shdn v2a v1a inva 20 19 18 16 15 13 12 11 invc v1c v2c v agnd v2d v1d invd 1 2 3 5 6 8 9 10 0.1 f 1562 f13a schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v frequency (khz) uses three r-c universal notches at f n = 133khz, 167khz, 222khz. detailed description in linear technology design note 195. wideband output noise 60 v rms ?20 ?0 ?0 ?00 20 0 ?0 ?0 1562 ta12b gain (db) 10 500 100 amplitude response amplitude response frequency (khz) 25 ?0 gain (db) ?0 ?0 ?0 ?0 ?0 ?0 ?0 ?0 0 100 175 1562 ta13b 10
25 ltc1562 typical applicatio n s u (advanced) r q1 95.3k r q3 392k r in1b 69.8k r in1a 140k v in r q2 182k r in3 536k c in3 27pf c in2 33pf r in2 249k r in4 301k c in4 56pf r q4 66.5k r22 226k r24 649k 0.1 f v out v + v v to pin 10 r21 324k r23 196k ltc1562 invb v1b v2b v + shdn v2a v1a inva 20 19 18 16 15 13 12 11 invc v1c v2c v agnd v2d v1d invd 1 2 3 5 6 8 9 10 0.1 f c in1 390pf 1562 f14a schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v 9th order 22khz lowpass elliptic filter frequency (khz) 5 ?0 gain (db) ?0 ?0 ?0 ?0 0 ?0 ?0 ?0 ?0 10 50 1562 ta14b 10 amplitude response frequency (khz) 1 ?0 noise + thd (db) ?0 ?0 ?0 ?0 10 20 1562 ta14c ?0 ?5 ?5 ?5 ?5 ?5 v in = 1.65v rms = 4.6v p-p v s = 5v noise + thd vs frequency
26 ltc1562 dual 5th order lowpass elliptic filter r q1 r q1 r in1b r in1a v in1 v in2 r q2 c in2 r in2 r in2 c in2 r q2 r22 r22 0.1 f v out2 v out1 5v ?v r21 r21 ltc1562 invb v1b v2b v + shdn v2a v1a inva 20 19 18 16 15 13 12 11 invc v1c v2c v agnd v2d v1d invd 1 2 3 5 6 8 9 10 0.1 f c in1 r in1b r in1a c in1 1562 ta15a schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v construction and instrumentation cautions 100db rejections at hundreds of kilohertz require electri- cally clean, compact construction, with good grounding and supply decoupling, and minimal parasitic capaci- tances in critical paths (such as operational filter inv inputs). in a circuit with 5k resistances trying for 100db rejection at 100khz, a stray coupling of 0.003pf around the signal path can preclude the 100db. (by comparison, the stray capacitance between two adjacent pins of an ic can be 1pf or more.) also, high quality supply bypass capacitors of 0.1 m f near the chip provide good decoupling from a clean, low inductance power source. but several inches of wire (i.e., a few microhenrys of inductance) from the power supplies, unless decoupled by substantial capacitance ( 3 10 m f) near the chip, can cause a high-q lc resonance in the hundreds of khz in the chips supplies or ground reference, impairing stopband rejection and other specifications at those frequencies. in demanding filter circuits we have often found that a compact, carefully laid out printed circuit board with good ground plane makes a difference of 20db in both stopband rejection and distor- tion performance. highly selective circuits can even ex- hibit these issues at frequencies well below 100khz. finally, equipment to measure filter performance can itself introduce distortion or noise floors; checking for these limits with a wire replacing the filter is a prudent routine procedure. f c (hz) r in1a r in1b c in1 r q1 r21 r in2 c in2 r q2 r22 100k 5.9k 7.5k 680pf 28k 7.5k 6.34k 68pf 9.31k 11.3k 75k 8.06k 15.4k 560pf 36.5k 13.3k 11.3k 68pf 12.7k 20k 50k 16.9k 35.7k 390pf 56.2k 30.1k 25.5k 68pf 18.7k 44.2k amplitude response frequency (khz) 120 ?0 ?0 100 20 0 ?0 ?0 1562 ta15b gain (db) 10 1000 100 f c = 100khz typical applicatio n s u (advanced)
27 ltc1562 information furnished by linear technology corporation is believed to be accurate and reliable. however, no responsibility is assumed for its use. linear technology corporation makes no represen- tation that the interconnection of its circuits as described herein will not infringe on existing patent rights. dimensions in inches (millimeters) unless otherwise noted. package descriptio n u g package 20-lead plastic ssop (0.209) (ltc dwg # 05-08-1640) g20 ssop 0595 0.005 ?0.009 (0.13 ?0.22) 0 ?8 0.022 ?0.037 (0.55 ?0.95) 0.205 ?0.212** (5.20 ?5.38) 0.301 ?0.311 (7.65 ?7.90) 1234 5 6 7 8910 0.278 ?0.289* (7.07 ?7.33) 17 18 14 13 12 11 15 16 19 20 0.068 ?0.078 (1.73 ?1.99) 0.002 ?0.008 (0.05 ?0.21) 0.0256 (0.65) bsc 0.010 ?0.015 (0.25 ?0.38) dimensions do not include mold flash. mold flash shall not exceed 0.006" (0.152mm) per side dimensions do not include interlead flash. interlead flash shall not exceed 0.010" (0.254mm) per side * **
28 ltc1562 1562f lt/tp 0199 4k ? printed in usa ? linear technology corporation 1998 linear technology corporation 1630 mccarthy blvd., milpitas, ca 95035-7417 (408) 432-1900 l fax: (408) 434-0507 l www.linear-tech.com typical applicatio n u amplitude response frequency (khz) 1 ?0 gain (db) ?0 0 20 10 100 300 1562 ta16b ?0 ?0 f c = 64khz f c = 16khz f c = 32khz related parts part number description comments ltc1068, ltc1068-x quad 2-pole switched capacitor building block family clock-tuned ltc1560-1 5-pole elliptic lowpass, f c = 1mhz/0.5mhz no external components, so8 ltc1562-2 quad 2-pole active rc, 20khz to 300khz same pinout as the ltc1562 f c (hz) r in1 = r in3 r21 = r23 r q1 = r q3 r in2 = r in4 r22 = r24 r q2 = r q4 16k 105k 105k 34k 340k 340k 34k 32k 26.1k 26.1k 16.9k 84.5k 84.5k 16.9k 64k 8.45k 6.49k 8.45k 16.2k 21k 8.45k 1v/div 10 m s/div 1562 ta16c dual 4th order 12db gaussian lowpass filter 1 2 3 5 6 8 9 10 20 19 18 16 15 13 12 11 inv b v1 b v2 b v + shdn v2 a v1 a inv a inv c v1 c v2 c v agnd v2 d v1 d inv d ltc1562 r in2 r in4 r in1 v in2 v in1 schematic includes pin numbers for 20-pin package. pins 4, 7, 14, 17 (not shown) also connect to v v out1 1562 ta16a v out2 r in3 5v r q1 r21 r23 0.1 f 1 f r q3 r24 r q4 r q2 r22 4-level eye diagram f c = 16khz, data clock = 32khz

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