Subscribe Recommend		Op-Amp Oscillator Design with the HP-67 Programmable Calculator This is my second HP-67 program, which I wrote to help me with the design of a project that is currently (Nov. 2008) in the planning stages. This program selects component values for an op-amp based relaxation oscillator, given the desired frequency and output wave form peak voltages. It can also solve the inverse problem, finding the frequency and voltages resulting from given component values. The following is the schematic for such an oscillator: R1 and R2 form a voltage divider, with an additional input from the op-amp output through R3. When the op-amp output is at a high-level, the voltage at the non-inverting input of the op-amp is higher than when the op-amp output is at a low level. When the output is high, capacitor C1 also charges through R4 until the voltage across it (which is applied to the op-amp's inverting input) reaches the voltage at the non-inverting input. At that time, the op-amp output goes low, and the capacitor begins to discharge through R4 until the voltage once again reaches the (now lower) voltage at the non-inverting input. If one were to monitor the op-amp output, it would alternate between a high level (VOH, generally close to positive supply voltage, VPOS) and a low level (VOL, generally close to negative supply voltage, VNEG). The duty cycle of this square wave depends on the relative time it takes to charge and discharge C1 through R4, which in turn depends on the low (VPL) and high (VPH) peak voltages that C1 cycles between (which in turn depend on R1, R2, and R3). Monitoring the voltage across C1 shows a triangle wave. With this program, you can select components for such an oscillator to achieve a desired frequency, and if it matters to your design, desired low and high triangle peaks (VPL and VPH). After the program computes the required component values, you can modify these values to match those actually available in the real world. The program will then compute what effect these changes have on the frequency and triangle peak voltages. The following equations describe the operation of the oscillator: You will first need to choose values for C1 and R1 arbitrarily, since for any desired frequency and given C1 and R1, it will be possible to find (possibly impractical) values for R2, R3, and R4. A good choice for R1 is generally somewhere around 10kΩ to 100kΩ. The choice of C1 depends on the frequency, and a readily available value near (50/f) μF is usually suitable. Using the Program First type in the program and save it, or read it from a previously recorded magnetic card. The card should be labelled as follows: OP-AMP OSCILLATOR DESIGN VNEG,VPOS VOL,VOH C1 R1 VPL,VPH f →%DC →R2→ →R3→ →R4→ Forward Solution: Finding R2, R3, and R4 Consider the following example: It is desired to find values for R2, R3, and R4 to produce an oscillator of about 2500Hz, with a triangle waveform that oscillates between 1.2V and 1.4V. The op-amp is to operate from a single 5V supply, and the op-amp's output is capable of a low of 0.3V and a high of 5V. Use a 0.022μF capacitor for C1, and a 22kΩ resistor for R1. Follow these steps to solve the problem: Description Keystrokes Display Select engineering notation   h  ENG   DSP 2   0.00  00  Enter power supply voltages  0 ENTER 5    f  a   0.00  00  Enter low and high level output voltages  0.3 ENTER 5    f  b   300. -03  Enter C1 (Farads)  0.022 EEx CHS 6    f  c   22.0 -09  Enter R1 (Ohms)  22 EEx 3    f  d   22.0  03  Enter desired triangle lower and upper voltage peaks  1.2 ENTER 1.4    f  e   1.20  00  Enter desired frequency (Hz)  2500   A   2.50  03  Compute square wave duty cycle  B   788. -03  Compute value of R2 (Ohms)  C   7.26  03  Compute value of R3 (Ohms)  D   123.  03  Compute value of R4 (Ohms)  E   71.4  03  Notes Specifying VOL and VOH is optional. If this step is omitted, the program will assume the op-amp output can span the entire negative and positive supply voltage range. If the triangle wave form peak voltages don't matter to your design (because you're only using the square wave output), you don't need to specify them. The program will assume peak voltages ranging from VOL+(VOH-VOL)/3 to VOH-(VOH-VOL)/3, which is the middle third of the op-amp output voltage range. This also happens to result in a 50% duty cycle. To achive a low duty cycle square wave, choose VPL and VPH close to the bottom of the op-amp output range (VOL). Likewise for a high duty cycle, choose VPL and VPH close to the top of the range (VOH). For the most stable oscillation frequency, choose VPL and VPH far away from the op-amp output voltage limits, VOL and VOH (to keep the triangle edges steep), and far away from each other (to keep any variations a small percentage of the overall voltage swing). Since these two goals are at odds with one another, a good compromise is to select VPL and VPH to span the middle of the VOL to VOH range (which is the default if VPL and VPH aren't specified). Reverse Solution: Finding VPL, VPH, Frequency, and Duty Cycle After finding the above ideal solution, we'll want to use real-world component values to build the physical circuit. The closest E-24 resistor values to those computed are: R2 = 7.5kΩ, R3 = 120kΩ, and R4 = 68kΩ. What effect will using these values have on the frequency, VPL, and VPH? These are the steps to find out: Description Keystrokes Display Enter new value for R2  7.5 EEx 3   C   7.50 03  Enter new value for R3  120 EEx 3   D   120. 03  Enter new value for R4  68 EEx 3   E   68.0 03  Compute resulting value for VPL   f  e   1.23 00  Compute resulting value for VPH  R/S   1.44 00  Compute resulting frequency  A   2.57 03  Other Uses for this Program The oscillator design facilitated by this program consists of two parts, a comparator with hysteresis, and a capacitor being charged and discharged by the comparator output through a resistor. The equations describing the comparator aspect of the circuit are not affected by those describing the behaviour of the resistor-capacitor network, so the program can be used to design such comparators for other applications. Here is a brief example of using this program to design a comparator: Assume we want to design a comparator operating from a +/-12V supply, whose output goes low when the voltage exceeds +2V, and goes high when the voltage subsequently drops below -3V. Assume the op amp used has an output that can swing to within 0.7V of the voltage limits. Use a 10kΩ resistor for R1. Follow these steps to solve the problem: Description Keystrokes Display Enter power supply voltages  12 CHS ENTER 12    f  a  -12.0 00  Enter low and high level output voltages  11.3 CHS ENTER 11.3    f  b  -11.3 00  Enter R1  10 EEx 3    f  d    10.0 03  Enter desired lower and upper switching points  3 CHS ENTER 2    f  e  -3.00 00  Compute value of R2  C    8.98 03  Compute value of R3  D    16.7 03  Now select the closest real-world resistor values for R2 and R3 and determine how that affects the switching points: Description Keystrokes Display Enter new value for R2  9.1 EEx 3   C    9.10 03  Enter new value for R3  16 EEx 3   D    16.0 03  Compute resulting lower switching point   f  e  -3.03 00  Compute resulting upper switching point  R/S    2.16 00  Additional Real-World Considerations The mathematical model used as the basis of this program assumes that VOL and VOH are constant, regardless of load. For sufficiently low current, this is close enough to true to be ignored. Thus it is important to use fairly high resistor values for R3 and R4 (10kΩ or bigger to be on the safe side). If the value of R3 computed by the program is too low, start with a higher value for R1. Similarly, if the value computed for R4 is too low, use a lower value for C1. Some op-amps have an open-collector output. This means that when the output is low, it is pulled low through an output transistor, but when the output is high, it is simply floating. Thus, a pull-up resistor is needed to pull the output high. The chosen pull-up resistor must meet two requirements: It must have a high-enough resistance that the output transistor can overcome the pull-up current when the output is low. It must have a low-enough resistance that it is not so large a percentage of the resistance of R3 or R4 that it throws off the solution. For the LM339 comparator that I often use in my designs, I've found that a 1kΩ resistor works well, together with R3 and R4 values about 100 times as much. As described above, use a higher value for R1 to achieve a higher value for R3, and use a lower value for C1 to achieve a higher R4. Program Listing Line Instruction Comments 001♦   LBL a  Store VNEG and VPOS 002  STO 6  VPOS 003  x↔y    004  STO 5  VNEG 005  x↔y  Fall through and initialize VOL and VOH to VNEG and VPOS 006♦   LBL b  Store VOL and VOH 007  CF 3    008  STO 8  VOH 009  x↔y    010  STO 7  VOL 011  −  Initialize VPL and VPH 012  3    013  ÷  (VOH-VOL)/3 014  RCL 7    015  x↔y    016  +    017  STO A  Set VPL = VOL + (VOH-VOL)/3 018  RCL 8    019  LSTx    020  −    021  STO B  Set VPH = VOH - (VOH-VOL)/3 022  CF 1    023  RCL 8  Leave VOL and VPH on stack as feedback to user 024  RCL 7    025  RTN    026♦   LBL c  Store C1 027  CF 3    028  STO C    029  RTN    030♦   LBL d  Store R1 031  CF 3    032  STO 1    033  RTN    034♦   LBL e  Store or compute (if necessary) VPL and VPH 035  F? 3  If data entered, store new VPL and VPH 036  GTO 9    037♦   LBL 1  Otherwise, compute VPL and VPH if necessary 038  F? 1  Need to compute VPL and VPH? 039  GTO 8    040  RCL B  Recall already-up-to-date VPL and VPH 041  RCL A    042  RTN    043  RCL B  If user presses R/S after seeing VPL, display VPH 044  RTN    045♦   LBL 8  Recompute VPL and VPH 046  RCL 1    047  RCL 3    048  ×    049  STO D    050  RCL 2    051  RCL 3    052  ×    053  ST I    054  +    055  RCL 2    056  RCL 1    057  ×    058  STO 9    059  +    060  1/x    061  STO E    062  RCL 5    063  ×    064  RCL D    065  ×    066  RCL E    067  RCL 6    068  ×    069  RC I    070  ×    071  +    072  STO D  Partial result common to VPL and VPH 073  RCL E    074  RCL 9    075  ×    076  STO E  End of computation common to VPL and VPH 077  RCL 7  Compute VPL 078  ×    079  +  End of computation of VPL 080  RCL E  Compute VPH 081  RCL 8    082  ×    083  RCL D    084  +  End of computation of VPH; VPL is in Y-register 085♦   LBL 9  Store entered or computed VPH and VPL 086  STO B  Store VPH 087  x↔y    088  STO A  Store VPL 089  CF 1  VPL and VPH are now up to date 090  RTN    091  RCL B  If user presses R/S after seeing VPL, display VPH 092  RTN    093♦   LBL B  Compute duty cycle 094  CF 3    095  GSB 7  Get numerator and denominator (also used for computing R4 or f) 096  LSTx  Numerator 097  x↔y    098  ÷    099  RTN    100♦   LBL 7  Compute denominator of duty cycle, leaving numerator in LSTx 101  GSB 1  Recompute VPL and VPH if necessary; leaves VPH in X, VPL in Y 102  RCL 8  Compute first half of denominator 103  −    104  RCL B    105  RCL 8    106  −    107  ÷    108  LN    109  RCL A  Compute second half of denominator (which is also the numerator) 110  RCL 7    111  −    112  RCL B    113  RCL 7    114  −    115  ÷    116  LN    117  +  Combine two halves, leaving numerator in LSTx 118  RTN    119♦   LBL A  Store or compute f 120  F? 3    121  GTO 0    122  GSB 7  Get denominator (also used for computing R4 and duty cycle) 123  RCL 4  Multiply by R4 and C1 124  ×    125  RCL C    126  ×    127  1/x    128♦   LBL 0  Store entered or computed f 129  STO 0    130  RTN    131♦   LBL C  Store or compute R2 132  F? 3    133  GTO 2    134  GSB 5  Compute numerator of R2 135  RCL 6  Compute denominator of R2 136  GSB 6    137  ÷    138  STO 2  Store computed R2 139  RTN    140♦   LBL 2  Store R2 and invalidate VPL and VPH 141  STO 2    142  SF 1  Must recompute VPL and VPH for user-defined R2 143  RTN    144♦   LBL D  Store or compute R3 145  F? 3    146  GTO 3    147  GSB 5  Compute numerator of R3 (same as R2) 148  RCL 6  Compute denominator of R3 149  RCL 5    150  −    151  ÷    152  RCL A    153  RCL B    154  −    155  ÷    156  STO 3  Store computed R3 157  RTN    158♦   LBL 3  Store R3 and invalidate VPLh and VPH 159  STO 3    160  SF 1  Must recompute VPL and VPH for user-defined R3 161  RTN    162♦   LBL E  Store or compute R4 163  F? 3    164  GTO 4    165  GSB 7  Get denominator (also used for computing f or duty cycle) 166  RCL 0    167  ×    168  RCL C    169  ×    170  1/x    171♦   LBL 4  Store entered or computed R4 172  STO 4    173  RTN    174♦   LBL 5  Compute numerator common to R2 and R3 175  GSB 1  Recompute VPL and VPH if necessary 176  RCL 5    177  GSB 6    178  RCL 1    179  ×    180  CHS    181  RTN    182♦   LBL 6  Compute (VOL - VPL - VOH + VPH) * X + VOH * VPL - VPH * VOL 183  RCL 7    184  RCL A    185  −    186  RCL 8    187  −    188  RCL B    189  +    190  ×  Multiply (VOL - VPL - VOH + VPH) by VPOS or VNEG (now in Y) 191  RCL 8    192  RCL A    193  ×    194  +    195  RCL B    196  RCL 7    197  ×    198  −    199  RTN    Registers and Flags Register Use  0  Frequency (Hz)  1,2,3,4  Resistors R1, R2, R3, and R4 (Ohms)  5,6  VNEG and VPOS (Volts)  7,8  VOL and VOH (Volts)  A,B  VPL and VPH (Volts)  C  Capacitor C1 (Farads)  9,D,E,I  Temporary registers Flag Meaning  1  VPL and VPH need to be recomputed  3  User supplied input Revision History 2008-Nov-26 — Initial release. 2009-May-25 — Fixed a bug that caused an error if one did not specify VPL and VPH. Changing R1 no longer forces VPL and VPH to be recomputed. 2009-Jun-11 — Fixed a bug where the data entry flag sometimes wasn't cleared even though there had been no data entry. Other HP Calculator Programs I've written programs for many of the HP calculators calculators in my collection. You may be interested in some of these: HP 35s Curve Fitting Matrix Multi-Tool HP-41C/CV/CX Low-Sensitivity Sallen-Key Filter Design Op-Amp Gain and Offset Stage Design Op-Amp Oscillator Design HP-67 Low-Sensitivity Sallen-Key Filter Design Op-Amp Gain and Offset Stage Design Resistor Networks of 1 or 2 Nodes     Buy Stefan a coffee! If you've found this article useful, consider leaving a donation to help support stefanv.com   Last updated Friday June 12, 2009. E-mail Stefan   Disclaimer: Although every effort has been made to ensure accuracy and reliability, the information on this web page is presented without warranty of any kind, and Stefan Vorkoetter assumes no liability for direct or consequential damages caused by its use. It is up to you, the reader, to determine the suitability of, and assume responsibility for, the use of this information. Copyright: All materials on this web site, including the text, images, and HTML mark-up, are Copyright © 2009 by Stefan Vorkoetter unless otherwise noted. All rights reserved. Unauthorized duplication prohibited. You may link to this site or pages within it, but you may not link directly to images on this site, and you may not copy any material from this site to another web site or other publication without express written permission. You may make copies for your own personal use.