1 application note 1556 building an accurate spice model for low noise, low power precision amplifiers abstract in today's fast moving competitive markets, more and more customers are requesting spice models to run comprehensive circuit simulations. system engineers are requiring increasingly accurate models for all types of integrated circuits. earlier spice models (1980) had to minimize the number of nonlinear elements to minimize simulation time, all at the cost of accuracy. today's models, thanks to the advancement of computing power, can increase the number of nonlinear elements and improve the accuracy of the models. the focus of this application note is to provide a method for developing a multi-stage spice model for low noise and low power operational amplifiers. the model presented, started with the work from mark alexander and derek f. bowers from analog devices (appnote an-138, 1990) [1]. the final model ended up with several key architectural changes that were required to model today's low noise, and low power precision amplifiers. this application note provides a systematic process that simplifies the understanding of how to build an accurate straightforward spice model. this is accomplished by a model architecture that processes the input signal through several stages. the model parameters can easily be calculated using a hand calculator or excel spreadsheet. the application note does not discuss the process of using spice, and assumes the user is familiar with this software. the model presented in this application note is the isl28127 single-pole 10mhz amplifier. the model enables the user to simulate important ac and dc parameters of an amplifier. for higher speed amplifiers, with multiple poles and zeros, reference an-138 [1]. the ac parameters incorporated into the model are: 1/f and flat-band noise, slew rate, cmrr, gain and phase. the dc parameters are vos, ios, total supply current and output voltage swing. the model uses typical (+25c) parameters given in the ?electrical specifications? table of the data sheet [2]. introduction the key to an accurate model is the input stage. the closer you model the input stage to the actual amplifier, the better your results. with only a few of the process parameters of the input stage transistors or mosfets, you can achieve very accurate ac representation of the amplifiers performance. another advantage of this model's architecture is the ability to model amplifiers with split supplies. there is no ground reference in any of the signal processing blocks. instead, after the differential to single-ended conversion, all internally generated node voltages are referenced to the mid point of the supplies, much like the actual operation of an amplifier. discussed in this application note are the following topics: 1. the different cascaded stages of the spice model: -voltage noise stage - input stage -1st gain stage -2nd gain stage - mid supply stage - supply isolation stage - common mode gain stage -output stage 2. how the vccs stages works 3. how the vccs output stage works 4. systematic process for calculating model parameters 5. simulation results. actual device vs simulation 6. conclusions cascaded stages figure 1 is the schematic for the spice model and figure 2 is the net list. notice from the schematic, the only circuitry resembling an am plifier is the input stage. all other stages process the input signal with voltage controlled current sources (vccs) and voltage controlled voltage sources (vcvs) along with diodes, dc supplies, simple resistors, capacitors and inductors. the circuit schematic is built from eight different functional blocks. each block is discussed in the following sections, with details of the blocks? functionality and design considerations. caution: these devices are sensitive to electrostatic discharge; follow proper ic handling procedures. 1-888-intersil or 1-888-468-3774 | intersil (and design) is a registered trademark of intersil americas inc. copyright intersil americas inc. 2010. all rights reserved all other trademarks mentioned are the property of their respective owners. april 19, 2010 an1556.0 author: don lafontaine
2 an1556.0 april 19, 2010 . figure 1. spice schematic v in - v out v+ v- + - + - + - + - + - d12 r17 377.4 ios 1e-9 r1 5e11 r2 5e11 dn 0.1v v5 in+ vin- vcm superb q1 q2 superb cascode cascode q4 q5 r3 4.45k r4 4.45k iee1 96e-6 d1 dx mirror q3 iee 200e-6 1 2 3 4 5 6 v ++ + - + - v in + 24 25 4 5 v ++ vc vmid v -- vcm + - vos 10e-6 + - + - d2 dx d3 dx v1 1.86v v2 1.86v g1 g2 r5 1 r6 1 4 5 v ++ 11 12 10 + - + - + - + - d4 dx d5 dx v3 1.86v v4 1.86v g3 g4 r7 572.9e6 r8 vg 14 13 c2 55.55pf c3 r9 1 r10 1 55.55pf 572.9e6 vmid vmid + - + - g5 g6 r11 1 r12 18 17 l1 3.18e-3 l2 3.18e-3 1 vcm eos + - + - isy 2.2ma v ++ v- v+ + - + - g7 g8 r15 90 r16 22 23 90 v -- vcm vc + - + - d10 dy d11 dy d8 dx d9 dx d6 dx d7 dx vg v ++ v -- v -- + - + - v5 v6 1.12v 1.12v vg + - + - vc g10 g9 vout 20 21 8 9 7 en voltage noise input stage 1 st gain stage mid supply ref 2 nd gain stage common mode gain stage supply isolation stage e2 e3 output stage c6 2pf c4 2.5pf c5 2.5pf application note 1556
3 an1556.0 april 19, 2010 * source isl28127_spicemodel * revision c, august 8th 2009 lafontaine * model for noise, supply currents, 150db f=50hz cmrr, *128db f=5hz aol *copyright 2009 by intersil corporation *refer to data sheet ?license statement? use of *this model indicates your acceptance with the *terms and provisions in the license statement. * connections: +input * | -input * | | +vsupply * | | | -vsupply * | | | | output * | | | | | .subckt isl28127subckt vin+ vin-v+ v- vout * source isl28127_spicemodel_0_0 * *voltage noise e_en in+ vin+ 25 0 1 r_r17 25 0 377.4 d_d12 24 25 dn v_v7 24 0 0.1 * *input stage i_ios in+ vin- dc 1e-9 c_c6 in+ vin- 2e-12 r_r1 vcm vin- 5e11 r_r2 in+ vcm 5e11 q_q1 2 vin- 1 superb q_q2 3 8 1 superb q_q3 v-- 1 7 mirror q_q4 4 6 2 cascode q_q5 5 6 3 cascode r_r3 4 v++ 4.45e3 r_r4 5 v++ 4.45e3 c_c4 vin- 0 2.5e-12 c_c5 8 0 2.5e-12 d_d1 6 7 dx i_iee 1 v-- dc 200e-6 i_iee1 v++ 6 dc 96e-6 v_vos 9 in+ 10e-6 e_eos 8 9 vc vmid 1 * *1st gain stage g_g1 v++ 11 4 5 0.0487707 g_g2 v-- 11 4 5 0.0487707 r_r5 11 v++ 1 r_r6 v-- 11 1 d_d2 10 v++ dx d_d3 v-- 12 dx v_v1 10 11 1.86 v_v2 11 12 1.86 * *2nd gain stage g_g3 v++ vg 11 vmid 4.60767e-3 g_g4 v-- vg 11 vmid 4.60767e-3 r_r7 vg v++ 572.958e6 r_r8 v-- vg 572.958e6 c_c2 vg v++ 55.55e-12 c_c3 v-- vg 55.55e-12 d_d4 13 v++ dx d_d5 v-- 14 dx v_v3 13 vg 1.86 v_v4 vg 14 1.86 * *mid supply ref r_r9 vmid v++ 1 r_r10 v-- vmid 1 i_isy v+ v- dc 2.2e-3 e_e2 v++ 0 v+ 0 1 e_e3 v-- 0 v- 0 1 * *common mode gain stage with zero g_g5 v++ vc vcm vmid 31.6228e-9 g_g6 v-- vc vcm vmid 31.6228e-9 r_r11 vc 17 1 r_r12 18 vc 1 l_l1 17 v++ 3.183e-3 l_l2 18 v-- 3.183e-3 * *output stage with correction current sources g_g7 vout v++ v++ vg 1.11e-2 g_g8 v-- vout vg v-- 1.11e-2 g_g9 22 v-- vout vg 1.11e-2 g_g10 23 v-- vg vout 1.11e-2 d_d6 vg 20 dx d_d7 21 vg dx d_d8 v++ 22 dx d_d9 v++ 23 dx d_d10 v-- 22 dy d_d11 v-- 23 dy v_v5 20 vout 1.12 v_v6 vout 21 1.12 r_r15 vout v++ 9e1 r_r16 v-- vout 9e1 * .model superb npn + is=184e-15 bf=30e3 va=15 ik=70e-3 rb=50 + re=0.065 rc=35 cje=1.5e-12 cjc=2e-12 + kf=0 af=0 .model cascode npn + is=502e-18 bf=150 va=300 ik=17e-3 rb=140 + re=0.011 rc=900 cje=0.2e-12 cjc=0.16e-12f + kf=0 af=0 .model mirror pnp + is=4e-15 bf=150 va=50 ik=138e-3 rb=185 + re=0.101 rc=180 cje=1.34e-12 cjc=0.44e-12 + kf=0 af=0 .model dn d(kf=6.69e-9 af=1) .model dx d(is=1e-12 rs=0.1) .model dy d(is=1e-15 bv=50 rs=1) .ends isl28127subckt figure 2. spice net list application note 1556
4 an1556.0 april 19, 2010 voltage noise stage the first stage in the model schematic, moving from left to right, is the voltage noise stage. this stage generates the 1/f and flat-band noise. to generate a flat-band voltage noise of a precision amplifier with only 4nv/ hz, all diodes and transistor model parameters kf (flicker noise coefficient) and af (flicker noise exponent) need to be set to zero. to lower the noise floor of the model to single digit nanovolts, it may be necessary to reduce the network's johnson noise [3] by reducing the resistance values where possible. before reducing the resistor values, the process is to calculate the standard resistor values and complete all simulation tweaks. once this is done, the last step is to tweak the voltage noise stage by dropping the resistor values to 1 while recalculating the g m and time constants of the stages to maintain the same transfer function for that stage. resistors r 5 , r 6 , and r 9 thru r 12 are resistors that can easily be set to 1 . for amplifiers with noise le vels in the flat-band range of 100's of nv, reducing the network's johnson noise may not be necessary. initial noise simulations will tell you if this step is necessary. with the model's flat-band noise set below the amplifier's noise floor, the user can now adjust the 1/f and flat-band noise with adjustments to dn, r 17 and v 5 . input stage the isl28127 was selected for this application note to illustrate the level of accuracy obtainable by modeling an amplifiers exact input structure. the input stage of the isl28127 consists of five bipolar transistors that model the actual device configuration, as shown in figure 1. this however will not be the case for most spice models. figure 3 and figure 4 show typical nmos and pmos input stages respectively. the input stage can be configured with the same type of input device (npn, pnp, p and n channel mosfets or j-fets) as the physical op amp being modeled. the input stage includes a current supply to model ios, a voltage supply to model vos and a vcvs along with r 1 and r 2 to account for cmrr of the device. 1st gain stage the purpose of the 1st gain stage is to set the combined gain of the input stage and the 1st gain stage to 1. setting the combined gains to 1 simplifies the calculation to determine the slew-rate limiting components in the 2nd gain stage. diodes d 2 and d 3 along with dc supplies v 1 and v 2 might be unnecessary, because their function is to clamp the output voltage swing and were going to do that in the next stage. we left them in because they're free. dc supply voltages v 1 and v 2 should be slightly larger than v 3 and v 4 in the 2nd gain stage. the thought is to limit most of the signal amplitude in the 1st stage and do the final amplitude tweak in the 2nd stage. 2nd gain stage the 2nd gain stage is wher e the avol, bandwidth and slew-rate of the amplifier are set using g 3 , g 4 , r 7 , r 8 , c 2 and c 3 . diodes d 4 and d 5 along with dc supplies v 3 and v 4 are used to set the maximum output voltage swing. mid supply reference stage the mid supply reference stage is simply two equal resistors r 9 and r 10 . these resistors are used to generate a mid supply reference voltage. the resistor values are set to 1 to reduce the johnson voltage noise of the model. the high current that flows through these resistors is transparent to the model user because of the supply isolation stage, more free stuff. figure 3. typical nmos input stage figure 4. typical pmos input stage application note 1556
5 an1556.0 april 19, 2010 common mode gain stage the common mode gain stage consists of two vccs's that drive two equal resistors in series with an inductor connected to the supply rails. the inductors simulate the typical fall-off of cmrr that most amplifiers exhibit as the input frequency is increased. the current sources are controlled by the input common mode voltage (generated by resistors r 1 and r 2 in the input stage) relative to the mid supply voltage. each control source has a g m equal to the reciprocal of the associated resistor value divided by the cmrr of the amplifier at dc (equation 10). the inductors add a zero to the common-mode gain, which is equivalent to adding a pole to the cmrr. the common-mo de voltage, after being scaled and appropriately freq uency shaped, is then added back into the input stage via the vcvs called eos. supply isolation stage the supply isolation stage consists of two vcvs's and a current source. this stage enables the user to program the total supply current of the amplifier with just one entry in the node list. it also isolates the internal supply currents from the external supply current seen by the user. this enables the model to provide the correct supply current for low power amplifiers with low voltage noise. output stage the operation of the output stage is not entirely obvious. the amplifier's output signal, after receiving all the appropriate frequency shaping, appears as a voltage referenced to mid supply at the inputs to g 7 and g 8 . g 7 and g 8 drive two equal resistors connected to the supply rails and act as active current generators. both g 7 and g 8 generate just enough curre nt to provide the desired voltage drop across its parallel resistor. refer to the section ?how the vccs output stage works? on page 6. when there is no load on the output, the model draws no current from either supply rail, thus behaving like an amplifier output. simulating the right output resistance means the dc open loop gain will be properly reduced as the amplifier is loaded. when a load is applied to the output, equal currents will be pulled from both supply rails. to make the output behave like a real amplifier, g 9 and g 10 force the appropriate amount of current to make it appear as if all the current is being sourced or sunk from the correct supply. output short circuit protection is provided by diodes d 6 and d 7 along with dc supplies v 5 and v 6 . under fault conditions, the output voltage is clamped to the previous frequency shaping stage. the output short circuit current limit is determined by adjusting the value of v 5 and v 6 . how the vccs stage works when the voltage at the inputs to g 1 and g 2 (figure 5) increases, the resultant voltage at the midpoint will rise. likewise, when the voltage at the inputs decrease, the midpoint voltage will decrease. if the g m of the stage is equal to the reciprocal of the parallel resistor, the stage has a positive unity gain. the single-ended equivalent circuit of figure 5 is shown in figure 6. the circuit shown in figure 6 is sometimes easier to help visualize the signal flow through the stages. figure 5. how the vccs works + - + - g1 g2 r5 1 ? r6 1 ? v ++ 11 12 10 + - v -- midpoint voltage + - input voltage goes up ? current goes up ? net current through r5 drops ? midpoint voltage goes up v + - input voltage goes up ? current goes up ? net current through r6 goes up ? midpoint voltage goes up figure 6. single-ended equivalent circuit to figure 5 + - r# 1 ? 12 + - v + - midpoint voltage application note 1556
6 an1556.0 april 19, 2010 how the vccs output stage works figure 7 explains how the output stage works for a steady input voltage, an increasing input voltage and a decreasing input voltage. a systematic process for calculating model parameters table 1 is a list of the amplifiers parameters required to calculate the model parameters. the values shown in the table are for the isl28127 model. once the values in table 1 are determined, the model parameters given in equations 1 through 15 can be calculated and put into the spice schematic. the following equations will determine the model parameters for the spice schematic. putting them into an excel spreadsheet will enable the user to change critical specs and quickly see the effect on the op amp performance. the calculations are given for each stage of the model. input stage and gain stage calculations the process to set the slew rate and unity gain bandwidth, for a single pole stage, is accomplished in 3steps: ? determine the capacitor value knowing iee and the slew rate (equation 1). this effectively sets the maximum frequency for the single pole rc network, and therefore the unity gain bandwidth. ? determine the resistor value knowing the dominant pole frequency (equation 2). this effectively sets the break point for the rc network. ? determine the g m of the vccs knowing the desired avol and r value of the rc network. step 1 iee is the value of the current source feeding the input differential pair (reference figure 1). under slew rate conditions, instantaneously all of this current is flowing through one side of the differential pair (until the feedback loop catches up). equation 1 is used to calculate the capacitor value to set the slew rate of the model. equation 1 is basically i c = cdv/dt , with slew rate equal to dv/dt and iee equal to i c . equation 2 calculates the value of the resistor for a set capacitor value of c 2,3 and dominant pole frequency fp1. step 2 where f p1 = dominant pole (reference figure 8). table 1. device parameters parameter value units comments quiescent supply current 2.2e-3 a vcc 15 v vee -15 v iee 200e-6 a differential input current source slew rate 3.6e6 v/sec fp1 5 hz dominant pole (figure 8) avol 2640e3 v/v 128.43db vos 1e-5 v ios 1e-9 a te m p e ra t u r e 2 5 c vt 0.0257 v differential input resistance 5e-11 default value if unknown cmrr 3.16e7 v/v 150db figure 7. how the vccs output stage works v out + - + - g7 g8 r15 90 ? r16 90 ? vout output stage + - + - v + - input voltage constant ? voltage drop across resistors equally oppose each other ? output voltage stays at mid supply input voltage goes up ? current reduces in r15 ? current increases in r16 ? midpoint voltage goes up input voltage goes up ? current increases in r15 ? current reduces in r16 ? midpoint voltage goes down fcm 50 hz common mode pole rout 45 isc 45 ma voh 13.7 v vout max vol -13.7 v vout max table 1. device para meters (continued) parameter value units comments c 2 c 3 iee slewrate ---------------------------- == (eq. 1) c 2 c 3 200 10 6 ? 3.6 10 6 ? ---------------------------- 55.55pf = == r 7 r 8 1 2 f p1 c 23 , --------------------------- - == (eq. 2) r 7 r 8 1 2 5 () 55.55pf () ------------------------------------------- - 572.958m = == application note 1556
7 an1556.0 april 19, 2010 figure 8 shows the relationship of the unity gain bandwidth to the dominant pole frequency and avol. step 3 once again, the 1st gain stage is used to set the combined gain of the input stage and the 1st gain stage to 1. the voltage required at the input of g 3 and g 4 to cause 200 x 10 -6 to flow through r 7 and r 8 is calculated in equation 4. during slew rate limit, the current through either resistor r 3 or r 4 will be clamped by the 200 x 10 -6 current sink. which resistor has the current depends upon the polarity of the input voltage (positive r 4 , negative r 3 ). this current will flow through the 4.45k resistor resulting in a voltage drop of (200 x 10 -6 ) x (4.45k ) = 890mv. this voltage drop appears at the input to g 1 and g 2 . in order to set the combined gain of the input stage and the 1st stage to one, we need to calculate the g m of g 1 and g 2 so their output voltage equals 43.4mv (equation 4) when 890mv is at their inputs. if we set the resistor value in parallel with the outputs of g 1 and g 2 to 1 , then the voltage will equal the current and we can write equation 5 to solve for the g m of g 1 and g 2 . if the design review document is not available, set r 3 and r 4 to 1 for the calculation of the voltage appearing at the inputs to g 1 and g 2 . equations 7 and 8 are used to set v 1 through v 4 voltages for the maximum output voltage swing. the output voltage will be clamped at a voltage equal to v ++ -(v 1,3 + v d2,d4 ) for positive input voltage swings and v -- + (v 2,4 + v d3,d5 ) for negative input voltage swings. where v t = 0.02585v at t = +25c. i s = 1 x 10-12 a (for both diodes). you can substitute some data sheet parameters directly into the model. these parameters are: eos = input offset voltage (dc component only). ios = input offset current. c diff = input differential capacitance (not shown in this model). common-mode gain stage where fcm is common-mode pole from the cmrr vs frequency curve (similar to the dominant frequency pole shown in figure 8). output stage setting the g m equal to the reciprocal of 2r out results in unity gain through g7-g10. the value of 2r out results from the need to have the output currents appear to be coming from one supply rail. simulation results figures 9 through 14 compare actual device performance to simulation results. for a complete set of comparisons, reference the data sheet [2]. figure 8. avol vs frequency g 3 g 4 avol r 78 , ---------------- - == (eq. 3) g 3 g 4 2640 6 10 572.958 6 10 --------------------------------- - 4.6 3 ? 10 = == g m i v --- - v g 34 , i g m ------- 200 6 ? 10 4.6 3 ? 10 ------------------------- 43.4mv == = ? = (eq. 4) g 1 g 2 g m i v --- - 43.4 10 3 890 10 3 ? ---------------------------- 48.77 10 3 ? == = ? = (eq. 5) r 3 r 4 4.45k = = from design review () (eq. 6) v 13 , v cc v outmax () ? v t ln 2i ee i s ------------ - ?? ?? ?? + = (eq. 7) v 24 , v ? outmax () v ee ? v t ln 2i ee i s ------------ - ?? ?? ?? + = (eq. 8) r 11 r 12 1m = = (eq. 9) g 7 g 8 1 r 11 12 , cmrr ------------------------------------------- = = (eq. 10) l 1 l 2 r 11 12 , 2 fp cm () -------------------------- = = (eq. 11) g 7 g 8 g 9 g 10 1 2r out ------------------- - == = = (eq. 12) r 15 r 16 2r out = = (eq. 13) v 3 i sc 0.764 () r out v t ln 20 10 6 i s ---------------------- ?? ?? ?? ? = (eq. 14) v 4 i sc 0.764 () r out v t ln 20 10 6 i s ---------------------- ?? ?? ?? ? = (eq. 15) application note 1556
8 an1556.0 april 19, 2010 characterization vs simulation results figure 9. characterized input noise voltage figure 10. simulated input noise voltage figure 11. characterized closed loop gain vs frequency figure 12. simulated cl osed loop gain vs frequency figure 13. characterized closed loop gain vs r f /r g figure 14. simulated closed loop gain vs r f /r g frequency (hz) 1 10 100 input noise voltage (nv/ hz) 0.1 1 10 100 1k 10k 100k v s = 19v a v = 1 frequency (hz) 1 10 100 input noise voltage (nv/ hz) 0.1 1 10 100 1k 10k 100k v(inoise) frequency (hz) gain (db) 100k 1m 10m 100m 10k 1k -10 0 10 20 30 40 50 60 70 100 a v = 1 a v = 100 a v = 1000 v s = 15v v out = 100mv p-p c l = 3.5pf r l = inf r g = 100, r f = 100k r g = 10k, r f = 100k a v = 10 r g = 1k, r f = 100k r g = open, r f = 0 frequency (hz) gain (db) 100k 1m 10m 100m 10k 1k -10 0 10 20 30 40 50 60 70 100 a v = 1 a v = 100 a v = 1000 r g = 10k, r f = 100k a v = 10 r g = open, r f = 0 r g = 1k, r f = 100k r g = 100, r f = 100k -5 -3 -1 1 3 5 7 9 11 13 15 frequency (hz) 100k 1m 10m 100m 10k 1k r f = r g = 100k r f = r g = 100 r f = r g = 10k r f = r g = 1k v s = 15v r l = 10k a v = +2 v out = 100mv p-p c l = 3.5pf normalized gain (db) -5 -3 -1 1 3 5 7 9 11 13 15 frequency (hz) 100k 1m 10m 100m 10k 1k v s = 15v r l = 10k a v = +2 v out = 100mv p-p c l = 3.5pf r f = r g = 100k r f = r g = 100 r f = r g = 10k r f = r g = 1k normalized gain (db) application note 1556
9 intersil corporation reserves the right to make changes in circui t design, software and/or specifications at any time without n otice. accordingly, the reader is cautioned to verify that the application note or technical brief is current before proceeding. for information regarding intersil corporation and its products, see www.intersil.com an1556.0 april 19, 2010 figure 15. characterized closed loop gain vs r l figure 16. simulated closed loop gain vs r l figure 17. characterized closed loop gain vs c l figure 18. simulated closed loop gain vs c l figure 19. characterized large signal 10v step response figure 20. simulated large signal 10v step response characterization vs simulation results (continued) -5 -4 -3 -2 -1 0 1 2 frequency (hz) normalized gain (db) 100k 1m 10m 100m 10k 1k v s = 15v a v = +1 v out = 100mv p-p c l = 3.5pf r l = 499 r l = 100 r l = 49.9 r l = 10k r l = 1k -5 -4 -3 -2 -1 0 1 2 frequency (hz) normalized gain (db) 100k 1m 10m 100m 10k 1k v s = 15v a v = +1 v out = 100mv p-p c l = 3.5pf r l = 499 r l = 100 r l = 49.9 r l = 10k r l = 1k frequency (hz) 100k 1m 10m 100m 10k 1k -3 -2 -1 0 1 2 3 4 5 6 7 v s = 15v r l = 10k a v = +1 v out = 100mv p-p c l = 1000pf c l = 220pf c l = 100pf c l = 25.5pf c l = 3.5pf normalized gain (db) normalized gain (db) frequency (hz) 100k 1m 10m 100m 10k 1k -3 -2 -1 0 1 2 3 4 5 6 7 v s = 15v r l = 10k a v = +1 v out = 100mv p-p c l = 25.5pf c l = 100pf c l = 220pf c l = 3.5pf c l = 1000pf -6 -5 -4 -3 -2 1 0 1 2 3 4 5 6 0 5 10 15 20 25 30 time (s) large signal (v) v s = 15v a v = 1 c l = 3.5pf v out = 10v p-p r f = 0, r g = inf r l = 2k r l = 10k -6 -5 -4 -3 -2 1 0 1 2 3 4 5 6 0 5 10 15 20 25 30 time (s) large signal (v) v s = 15v a v = 1 c l = 3.5pf v out = 10v p-p r f = 0, r g = inf r l = 10k application note 1556
10 an1556.0 april 19, 2010 conclusions this application note has presented a method for building an accurate straightforward spice model for today's low noise and low power precision amplifiers. the extremely close simulation to actual part comparison results was achieved by taking advantage of today's improved computing power and modeling 5 bipolar transistors with their specific model parameters for each type of transistor. improvements to previous models include the ability to model single digit nanovolt noise parameters and very low total system supply currents for micro-powered amplifiers. acknowledgment i would like to thank oscar mansilla for all his help with the spice software, and especially his help with generating sub-circuits from a node list and building my own libraries in spice. i would also like to thank bob pospisil for his technical expertise with op amps and helping me solve various problems along the way. references [1] mark alexander and derek f. bowers, application note an-138, ?spice-compatible op amp macro- models?, analog devices. [2] isl28127, isl28227 fn6633 intersil data sheet http://www.intersil.co m/data/fn/fn6633.pdf . [3] derek f. bowers, ieee 1989, ?minimizing noise in analog bipolar circuit design?, precision monolithics, inc. figure 21. simulated open-loop gain, phase vs frequency figure 22. simulated open-loop gain, phase vs frequency figure 23. characterized cmrr vs frequency figure 24. simulated cmrr vs frequency characterization vs simulation results (continued) open loop gain (db)/phase () frequency (hz) -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 0.1m 1m 10m 100m 1 10 100 1k 10k 100k 1m 10m 100m r l = 10k simulation c l = 10pf gain phase 0.1hz 10hz 1.0k 100k 10m -100 -50 0 50 100 150 200 frequency (hz) open loop gain (db)/phase () phase gain r l = 10k model v os set to c l = 10pf zero for this test 0 cmrr (db) 100 1k 10k 100k 1m 10m frequency (hz) 10 20 40 60 80 100 120 -10 10 30 50 70 90 110 130 r l = inf a v = +1 v cm = 1v p-p c l = 5.25pf v s = 15v v s = 2.25v v s = 5v 10m 1.0hz 100hz 10k 1.0m 100m 10g 1.0t -50 0 50 100 150 frequency (hz) cmrr (db) generated using full model. cmrr delta input base voltage/v cm input voltage application note 1556
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