AN2223 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator Author: Dave Van Ess Associated Project: Yes Associated Part Family: CY8C24xxx, CY8C27xxx, CY8C28xxx, CY8C29xxx Software Version: PSoC Designer™ 5.1 SP1.1 Related Application Notes: AN2041, AN2168, AN16833, AN2155 Abstract A switched capacitor integrator can approximate the functionality of an opamp. You do this by exploring the opamp’s characteristics and learn how they are similar to an integrator. Next you create an integrator (a faux opamp) using ® PSoC 1 switched capacitor blocks. Examples of a voltage follower and a programmable gain amplifier demonstrate the use of a faux opamp in real-world applications. Introduction Figure 1. The Ideal Opamp Opamps have simplified circuit design for engineers. They form a basic building block for the analog and mixed-signal design. PSoC 1 analog blocks, both continuous time (CT) and switched capacitor (SC) do not have a native opamp mode. They are wired so that they can create PGAs, insamps, filters, integrators, and so on. However, in some designs you only need a plain opamp. This application note shows you how to configure a SC block so that it approximates the functionality of an opamp. You see: The ideal opamp has the following characteristics: A brief explanation of how an opamp works. Infinite gain An explanation of how a SC integrator can emulate an opamp (faux opamp). Infinite bandwidth Examples of faux opamp circuits. Infinite input impedance This application note does not give in depth information about SC blocks. For more information see AN2041 – Understanding PSoC 1 Switched Capacitor Analog Blocks. Zero output impedance Zero input offset error Zero phase delay Zero noise Opamp Primer: The Ideal Opamp Zero power consumption An ideal opamp is shown is Figure 1. Zero cost Available off-the-shelf everywhere Free shipping for any size order They are fabricated from Utopian Nitrate and are packaged in Impossibilium. The Ideal opamp is only a model to help with the design and analysis of opamp circuits. www.cypress.com Document No. 001-33763 Rev. *D 1 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator Figure 3. Typical Integrator Bode Plot Opamp Golden Rules From the ideal opamp characteristics two golden rules are obtained that simplify the analysis of opamp circuits. The output attempts to do whatever is necessary to make the voltage difference between its inputs zero. The inputs draw no current. Gain If there is a negative feedback: Real World Compensated Opamp In the real world opamps are not ideal; they have many non-idealities such as finite gain and phase delay. Phase delay can introduce instability into opamp circuits. To reduce the possibility of instability (oscillations), most widely used commercial opamps have frequency compensation. This reduces the chance of oscillation when the opamp is connected in a feedback network. A Bode plot of a generic compensated opamp is shown in Figure 2. Gain Differential Switched Capacitor Integrator Open Loop Gain Figure 4. Differential Input SC Integrator φ1 VinA CA VinB GBW The compensated opamp has an open loop DC Gain and rolls off to unity gain at a frequency known as the gain bandwidth (GBW). A compensation pole is located at GBW/Gain. The transfer function is shown in Equation 1. Gain s 1+ GBW 2π Gain Equation 1 Equation 1 and Figure 2 show that the compensated opamp is actually a high gain low pass filter (LPF). Due to this an opamp can also be considered as an integrator with saturated gain at lower frequencies. Equation 2 shows the simplified transfer function; Figure 3 shows the typical integrator Bode plot. 2πGBW s www.cypress.com Equation 2 CF φ2 φ2 CB φ2 Frequency H ( s) ≈ For frequencies greater than the roll off point, the transfer function and bode plot of an opamp approximate an integrator. For closed-loop control circuits, an integrator can be used in place of an opamp. An integrator can be created in PSoC 1 SC blocks; its implementation is shown in Figure 4. Figure 2. Typical Opamp Bode Plot H (s) = Frequency φ1 Vout φ1 The transfer function is shown in Equation 3. f s Ci CF H (s) ≈ s : C =C =C A B i Equation 3 Since SC integrators can function as opamps but actually are not opamps, we refer to them as faux opamps. For more information on SC blocks see AN2041 ® Understanding PSoC 1 Switched Capacitor Analog Blocks. As stated earlier, the opamp embedded in the SC block cannot natively be used as a standalone opamp. Thus the need for an SC integrator that approximates the functionality of an opamp in closed-loop systems is a must. Document No. 001-33763 Rev. *D 2 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator Figure 5. Voltage Follower Schematic Programmable GBW Combining equations 2 and 3 produces the GBW value for a SC integrator, shown in Equation 4. GBW = f s Ci 2π CF Equation 4 VinA The SC block power settings and bias levels determine the maximum sample frequency (fs). Table 1 shows the maximum sample frequency for all six power and bias settings. These settings are configured in the global resources window of PSoC Designer. Power is set by changing the analog power setting; bias is changed by changing the opamp bias setting. Table 1. Power Settings Power Setting CA CF PSoC φ2 φ2 P0.3 P2.3 Changing the values of Ci (CA CB), CF, or fs alters the GBW. Flexible control of GBW enables you to design a stable closed-loop feedback system. φ1 P2.1 CB φ2 VinB Vout φ1 φ1 ASC10 With negative feedback established, the output must become equal to the VinA for the input difference to be zero; remember the golden opamp rules discussed earlier. To create a faux opamp an SCBLOCK needs to be placed in a PSoC Designer project. The SCBLOCK is located in the generic folder of the user module catalog. Figure 6 is an example of the user module placement. Max fs High Power High Bias 4 MHz High Power Low Bias 2 MHz Medium Power High Bias 1 MHz Medium Power Low Bias 500 kHz Low Power High Bias 250 kHz Low Power Low Bias 125 kHz Figure 6. Faux Opamp User Module Placement Examples Now that we have covered how a SC integrator can act as an opamp, we are going to go through a few examples of how this faux opamp can be used in real world applications. Included with this application note is a basic example project that the reader can use to implement the examples discussed as following. Example I (Voltage Follower) In this example the faux opamp acts as a voltage follower or buffer. VinA is the Non-Inverting input and VinB is the Inverting Input. To create the voltage follower/buffer the output needs to be fed back to VinB. The schematic for the follower is shown in Figure 5. www.cypress.com The SCBLK user module should be configured as shown in Figure 7. Document No. 001-33763 Rev. *D 3 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator Figure 7. Parameter Selections for FAUX SCBlock Figure 8. Global Resources For more information on these configuration settings refer to AN2041 – Understanding PSoC 1 Switched Capacitor Analog Blocks Using Equation 4 as a template, the parameters are plugged in to determine GBW. The calculation is shown in Equation 5. The following system parameters must be set: GBW = 1. 2. Ref Mux to (Vdd/2) +/- (Vdd/2). This sets AGND to Vdd/2. For more information on the Ref Mux and the meaning of the different settings see: AN2219 ® PSoC 1 Selecting Analog Ground and Reference. Set VC1 to 4 MHz. This value is selected as the column clock frequency. fs = f cc 4.0 MHz = = 1MHz 4 4 Equation 5 The global resource parameters are shown in Figure 8. f s Ci 1MHz 26 = = 129kHz 2π C F 2π 32 Equation 6 When this project is actively running, the output voltage can be measured at Vout (P0[3]). The output voltage follows the input voltage (P2[1]). The faux opamp is useful in a classical voltage follower just as the typical opamp is. However, the faux opamp has other advantages, such as programmable bandwidth and programmable gain. The following examples highlight some other features of the faux opamp that go beyond the traditional opamp. Differential Input Capacitors All the analysis until now has been done with the input capacitors ( C A , C B ) equally weighted. Doing so causes the opamp golden rules to apply. However, if the inputs have different weights, then the output attempts to make the differential input capacitor charge transfer zero. This is expressed in Equation 6. VinA C A − VinB C B = 0 Equation 7 Example II (Programmable Gain) In the previous example the output voltage followed the input. For this example we want the output voltage to be double the input voltage. Remember that the output is relative to AGND (Vdda/2). Equation 7 shows how to calculate the output voltage. www.cypress.com Document No. 001-33763 Rev. *D 4 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator Vout = AGND + (Vin − AGND) CA CB Figure 10. Switched Polarity Component Equation 8 To get 2x gains, the input capacitors need to be sized correctly CA = 26 CB = 13 These two parameters are changed as shown in Figure 9. Figure 9. Parameter Selection Voltage Doubler Out The new faux opamp golden rule must be expanded to reflect this change. It is shown in Equation 9. AsignVinAC A − VinB C B = 0 Equation 10 Example III (Programmable Gain with Polarity) With the new opamp shown in Figure 10, you can create negative gain. For this example, a gain of –2 needs to be applied to the input. For this configuration the output follows Equation 10. Vout = AGND + ASign (Vin − AGND) CA CB Equation 11 Looking at the previous example it is known how to get a gain of 2. All you need to do is switch the polarity of the A input. One solution is: CA = 26 CB = 13 When this project is actively running, the output follows equation 7 with the parameters set in Figure 9. The GBW is determined by the value of the capacitor connected to the feedback path. It is calculated in Equation 8. GBW = f s C B 1MHz 13 = = 64.7 kHz 2π C F 2π 32 Asign = neg These three parameters are changed as shown in Figure 11. Figure 11. Parameter Selection –2 gain Equation 9 You can change the input capacitors to create a wide variety of input-to-output voltage ratios; creating a programmable gain amplifier out of SC blocks. Changing Input Polarity An opamp cannot have two negative inputs. However, a faux opamp can. The SC blocks allow for switching the polarity of VinA. This results in the component shown in Figure 10. www.cypress.com Document No. 001-33763 Rev. *D 5 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator When this project is actively running, the output voltage follows Equation 10, using the parameters from Figure 11. Now you can create a programmable gain and polarity amplifier with the faux opamp. A transistor can be added to the output as shown in Figure 12 to increase the current capacity of the output, thus creating a programmable power supply. Figure 12. Programmable Power Supply Refhigh φ1 VinA CA CF P0.3 VinB P2.3 CB φ2 Equation 12 Rshunt Note that the VinA input does not have to come from an external source. It can be tied to an internal voltage like RefHi, or the output of a VDAC. SC blocks are easily configured as integrators. The integrator then functions as an opamp. Parameterization of the capacitor values and sample frequency enables precise control of GBW. Intentional misbalancing of the input capacitor and adjusting the polarity of the VinA input enables some unique PSoC applications. Vout φ1 I out = CA CB Summary PSoC φ2 φ2 AGND + Asign (Vin − AGND) φ1 ASC10 About the Author You can create a programmable current source by adding a shunt resistor to the emitter of the transistor as shown in Figure 13. Name: Dave Van Ess Title: Member of Technical Staff, Applications Engineer, Cypress Semiconductor [email protected] Figure 13. Programmable Current Source Refhigh φ1 VinA CA CF Contact: PSoC Load φ2 φ2 I out P0.3 CB VinB P2.3 φ2 φ1 Rshunt φ1 ASC10 The shunt resistor causes the output voltage to be converted into current. This current is available at the collector of the transistor. The output current is determined by the parameters in Equation 11. www.cypress.com Document No. 001-33763 Rev. *D 6 PSoC® 1 – Approximating an Opamp with a Switched Capacitor Integrator Document History ® Document Title: PSoC 1 – Approximating an Opamp with a Switched Capacitor Integrator – AN2223 Document Number: 001-33763 Revision ECN Orig. of Change Submission Date Description of Change ** 1499983 MAXK 10/04/2007 New application note. *A 2678525 TDU 03/25/2009 Updated software version and associated PSoC project 3253271 TDU 05/13/2011 Updated Project to 5.1, Fixed Grammar and Structure of AN, Updated Title and Abstract to better reflect contents of AN, and Updated Template. 3441042 TDU 11/21/2011 *B *C Template update Updated Project files *D 4382168 www.cypress.com MQY 05/16/2014 Sunset review. Minor copy editing. Removed link on Pg. 8 to Optical Navigation Sensors. 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The inclusion of Cypress’ product in a life-support systems application implies that the manufacturer assumes all risk of such use and in doing so indemnifies Cypress against all charges. Use may be limited by and subject to the applicable Cypress software license agreement. www.cypress.com Document No. 001-33763 Rev. *D 8