Op-Amp Oscillator Design with the HP-41C Programmable Calculator

May 25, 2009

I originally wrote this program for the HP-67 calculator, and then ported it to the HP-41C series. 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      ENG 2   0.00  00 
Enter power supply voltages  0 ENTER 5 
    
 0.00  00 
Enter low and high level output voltages  0.3 ENTER 5 
    
 300. -03 
Enter C1 (Farads)  0.022 EEx CHS 6 
    
 22.0 -09 
Enter R1 (Ohms)  22 EEx 3 
    
 22.0  03 
Enter desired triangle lower and upper voltage peaks  1.2 ENTER 1.4 
    
 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+(VOHVOL)/3 to VOH-(VOHVOL)/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       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 
    
-12.0 00 
Enter low and high level output voltages  11.3 CHS ENTER 11.3 
    
-11.3 00 
Enter R1  10 EEx 3 
    
  10.0 03 
Enter desired lower and upper switching points  3 CHS ENTER 2 
    
-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      -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:

  1. It must have a high-enough resistance that the output transistor can overcome the pull-up current when the output is low.

  2. 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
01♦   LBL “OSC”   
02♦   LBL a  Store VNEG and VPOS
03  STO 06  VPOS
04  x↔y   
05  STO 05  VNEG
06  x↔y  Fall through and initialize VOL and VOH to VNEG and VPOS
07♦   LBL b  Store VOL and VOH
08  CF 22   
09  STO 08  VOH
10  x↔y   
11  STO 07  VOL
12  −  Initialize VPL and VPH
13  3   
14  ÷  (VOHVOL)/3
15  RCL 07   
16  x↔y   
17  +   
18  STO 11  Set VPL = VOL + (VOHVOL)/3
19  RCL 08   
20  LASTx   
21  −   
22  STO 12  Set VPH = VOH – (VOHVOL)/3
23  CF 01   
24  RCL 08  Leave VOL and VPH on stack as feedback to user
25  RCL 07   
26  RTN   
27♦   LBL c  Store C1
28  CF 22   
29  STO 13   
30  RTN   
31♦   LBL d  Store R1
32  CF 22   
33  STO 01   
34  RTN   
35♦   LBL e  Store or compute (if necessary) VPL and VPH
36  FS?C 22  If data entered, store new VPL and VPH
37  GTO 09   
38♦   LBL 01  Otherwise, compute VPL and VPH if necessary
39  FS? 01  Need to compute VPL and VPH?
40  GTO 08   
41  RCL 12  Recall already-up-to-date VPL and VPH
42  RCL 11   
43  RTN   
44  RCL 12  If user presses R/S after seeing VPL, display VPH
45  RTN   
46♦   LBL 08  Recompute VPL and VPH
47  RCL 01   
48  RCL 03   
49  ×   
50  STO 14   
51  RCL 02   
52  RCL 03   
53  ×   
54  STO 10   
55  +   
56  RCL 02   
57  RCL 01   
58  ×   
59  STO 09   
60  +   
61  1/x   
62  STO 15   
63  RCL 05   
64  ×   
65  RCL 14   
66  ×   
67  RCL 15   
68  RCL 06   
69  ×   
70  RCL 10   
71  ×   
72  +   
73  STO 14  Partial result common to VPL and VPH
74  RCL 15   
75  RCL 09   
76  ×   
77  STO 15  End of computation common to VPL and VPH
78  RCL 07  Compute VPL
79  ×   
80  +  End of computation of VPL
81  RCL 15  Compute VPH
82  RCL 08   
83  ×   
84  RCL 14   
85  +  End of computation of VPH; VPL is in Y-register
86♦   LBL 09  Store entered or computed VPH and VPL
87  STO 12  Store VPH
88  x↔y   
89  STO 11  Store VPL
90  CF 01  VPL and VPH are now up to date
91  RTN   
92  RCL 12  If user presses R/S after seeing VPL, display VPH
93  RTN   
94♦   LBL B  Compute duty cycle
95  CF 22   
96  XEQ 07  Get numerator and denominator (also used for computing R4 or f)
97  LASTx  Numerator
98  x↔y   
99  ÷   
100  RTN   
101♦   LBL 07  Compute denominator of duty cycle, leaving numerator in LSTx
102  XEQ 01  Recompute VPL and VPH if necessary; leaves VPH in X, VPL in Y
103  RCL 08  Compute first half of denominator
104  −   
105  RCL 12   
106  RCL 08   
107  −   
108  ÷   
109  LN   
110  RCL 12  Compute second half of denominator (which is also the numerator)
111  RCL 07   
112  −   
113  RCL 11   
114  RCL 07   
115  −   
116  ÷   
117  LN   
118  +  Combine two halves, leaving numerator in LSTx
119  RTN   
120♦   LBL A  Store or compute f
121  FS?C 22   
122  GTO 00   
123  XEQ 07  Get denominator (also used for computing R4 and duty cycle)
124  RCL 04  Multiply by R4 and C1
125  ×   
126  RCL 13   
127  ×   
128  1/x   
129♦   LBL 00  Store entered or computed f
130  STO 00   
131  RTN   
132♦   LBL C  Store or compute R2
133  FS?C 22   
134  GTO 02   
135  XEQ 05  Compute numerator of R2
136  RCL 06  Compute denominator of R2
137  XEQ 06   
138  ÷   
139  STO 02  Store computed R2
140  RTN   
141♦   LBL 02  Store R2 and invalidate VPL and VPH
142  STO 02   
143  SF 01  Must recompute VPL and VPH for user-defined R2
144  RTN   
145♦   LBL D  Store or compute R3
146  FS?C 22   
147  GTO 03   
148  XEQ 05  Compute numerator of R3 (same as R2)
149  RCL 06  Compute denominator of R3
150  RCL 05   
151  −   
152  ÷   
153  RCL 11   
154  RCL 12   
155  −   
156  ÷   
157  STO 03  Store computed R3
158  RTN   
159♦   LBL 03  Store R3 and invalidate VPLh and VPH
160  STO 03   
161  SF 01  Must recompute VPL and VPH for user-defined R3
162  RTN   
163♦   LBL E  Store or compute R4
164  FS?C 22   
165  GTO 04   
166  XEQ 07  Get denominator (also used for computing f or duty cycle)
167  RCL 00   
168  ×   
169  RCL 13   
170  ×   
171  1/x   
172♦   LBL 04  Store entered or computed R4
173  STO 04   
174  RTN   
175♦   LBL 05  Compute numerator common to R2 and R3
176  XEQ 01  Recompute VPL and VPH if necessary
177  RCL 05   
178  XEQ 06   
179  RCL 01   
180  ×   
181  CHS   
182  RTN   
183♦   LBL 06  Compute (VOLVPLVOH + VPH) * X + VOH * VPLVPH * VOL
184  RCL 07   
185  RCL 11   
186  −   
187  RCL 08   
188  −   
189  RCL 12   
190  +   
191  ×  Multiply (VOLVPLVOH + VPH) by VPOS or VNEG (now in Y)
192  RCL 08   
193  RCL 11   
194  ×   
195  +   
196  RCL 12   
197  RCL 07   
198  ×   
199  −   
200  RTN   

Registers and Flags

Register Use
 00  Frequency (Hz)
 01,02,03,04  Resistors R1, R2, R3, and R4 (Ohms)
 05,06  VNEG and VPOS (Volts)
 07,08  VOL and VOH (Volts)
 11,12  VPL and VPH (Volts)
 13  Capacitor C1 (Farads)
 09,14,15,10  Temporary registers
Flag Meaning
 01  VPL and VPH need to be recomputed
 22  User supplied input

Revision History

2009-May-25 — Initial release of HP-41C/CV/CX version.

2009-Jun-11 — Fixed a bug where the data entry flag sometimes wasn’t cleared even though there had been no data entry.

2015-Jun-23 — Fixed a bug in the subroutine for computing the denominator of the duty cycle, wherein VPL and VPH were accidentally interchanged. Bug was in web-site listing only, not in original program.

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