Simple Method To Determine Esr Requirements For Stable
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This document discusses a simple method to determine the essential stability parameters for linear regulators and voltage references using a single non-invasive measurement. It explains that manufacturers often provide incomplete or inaccurate data, and real systems are more complex than typical datasheets. The method involves using a current injector and impedance analyzer to measure the output impedance with and without a capacitor. This allows extracting the key parameters of output inductor Lo, series resistance Rs, and parallel resistance Rp that are needed to assess phase margin and stability. In practice, in-circuit measurements can be more complicated by high quality factor resonances that obscure these parameters.
Simple Method To Determine Esr Requirements For Stable
- 1. Simple Method to Determine ESR Requirements for Stable Regulators A single non-invasive measurement provides all of the information needed to determine stable solutions
- 2. Define the Problem Many, if not most linear regulator and voltage reference circuits we evaluate fail to meet minimum stability criteria, resulting in several different issues •Failure to meet WCCA guidelines •Degraded circuit performance •Output impedance and transient response •Reverse transfer and crosstalk issues •Increased noise •Degraded PSRR •Potential for EMI issues
- 3. Other complicating factors Much of the manufacturer provided data is provided under ideal conditions Manufacturers data is often large signal not small signal data The manufacturers have different standards than we do for phase margin Real systems are much more complex than the typical data sheet Application circuits •Ferrite beads •Many distributed capacitors •Wide load current range
- 4. Understanding the Stability Issue Rp Voltage references and regulators Lo Rs (and Opamps also!) have regions where the output impedance appears Cout resistive and regions that appear Vout inductive ESR The inductance, Lo and the output Capacitor, Cout form a series tuned resonant circuit. The Q of the circuit is limited by resistors Rs, ESR and Rp. Phase margin and Q are related parameters
- 5. A Voltage Reference Example The device manufacturers either provide insufficient information or in some cases incorrect information Output Z with and without 0.1uF 10 2 10 1 TR1 10 0 10 -1 10 -2 102 103 104 105 106 f/Hz Recommended circuit TR1: Mag(Gain) TR1(Memory): Mag(Gain) Yields 9° Phase Margin Step Load with and without 0.1uF PSRR with and without 0.1uF 100 80 TR1/dB 60 40 20 102 103 104 105 106 107 f/Hz TR1: Mag(Gain) TR1(Memory): Mag(Gain)
- 6. Making the Measurement A Picotest J2111A current injector Modulates the regulator. A precision current monitor allows the output Input Regulator Power In DUT Out impedance to be measured easily. Out Vout Filter & Load Monitor The Bode 100 analyzer software can Modulation Mod Out assess the phase margin automatically as a cursor measurement J2111A Solid State Current Injector Power -- Custom High PSRR Adapter In an ideal world, we could measure the regulator without any output capacitors in order to obtain the inductance and resistances at the minimum operating load current. This allows simple extraction of the 3 parameters – Lo, Rs and Rp
- 7. Not All Regulators are created equal And so we measure them – preferably in circuit 10 2 10 1 The series resistance and the 10 0 series inductance can be TR1 drastically different between 10 -1 regulators. 10 -2 10 -3 102 103 104 105 106 107 f/Hz TR1: Mag(Gain) TR1(Memory): Mag(Gain) Same reference at 2 operating currents LM317 vs our custom regulator 10 2 The series resistance and the TR1/Ohm series inductance can also be 10 1 drastically different for the same device at different operating 10 0 currents. 10 -1 102 103 104 105 106 107 f/Hz TR1: Mag(Impedance) TR1(Memory): Mag(Impedance)
- 8. Extracting the Parameters Rp 10 0 TR1 10 -1 Lo 10 -2 Rs 101 102 103 104 105 106 f/Hz TR1(Memory): Mag(Gain) Without any capacitors, it is simple to extract the parameters
- 9. Not Always That Simple An in-circuit measurement from a real circuit board reveals a high Q resonance, making it difficult to see the L or the Rp, though we can See Rs=0.1 Ohms Using 3dB point -> Lo=0.1/(2*PI*2.85kHz) -> 5.5uH C=1/(Lo*(2*PI*Fo)^2) -> 8uF 20 vdb2 21 vdb2#11 R3 15.0 21 2.5 20 5.00 vdb2#11, vdb2 in db(volts) Lo Rs L2 5.5u 0.1 64n V2 Plot1 1 4 2 -5.00 Cout I1 8u AC = 1 3 -15.0 ESR 80m -25.0 10 100 1k 10k 100k 1Meg 10Meg frequency in hertz
- 10. Relating the measurement to minimum required ESR i 1 Lo i Rp Lo ESR( P M Cout Lo Rs Rp) Re Rs 2 2 cos P M Lo i Rp Lo Cout Cout 180 A simpler equation results, if we set the phase margin to 60 Degrees and solve for MINIMUM ESR. Lo Rs Rp Co ut Lo Rp Co ut Co ut ESR Rp Co ut
- 11. A Solution 1 vdb2 2 vdb2#1 15.0 Rp=2.5 Rs=0.1 Lo=5.5uH Cout=8uF 1 2 5.00 vdb2, vdb2#1 in db(volts) Lo Rs Rp Co ut Lo Rp Co ut Co ut Plot1 -5.00 ESR Rp Co ut -15.0 ESR 0.454 -25.0 1 v2 Step Load with ESR=80mΩ and 454m Ω 2 v2#2 10 100 1k 10k 100k 1Meg 10Meg frequency in hertz 700m R3 2.5 500m v2#2, v2 in volts Lo Rs L2 5.5u 0.1 64n V2 Plot1 300m 1 4 2 Cout I1 8u AC = 1 100m 2 1 3 ESR 454m -100m 20.0u 60.0u 100u 140u 180u time in seconds
- 12. There are Many Solutions •There are many solutions, each resulting in a different output impedance •The worst stability generally occurs at the minimum load current •Larger output capacitance results in lower impedance, but generally presents lower ESR •ESR does NOT have to be in series with the CAP, it can also be in series with the regulator 0.5 3 0.4 A single solution 0.3 2 can be selected ESR( Cout ) Zout ( Cout ) 0.2 based on a target 0.1 1 output impedance 0 0.1 0 6 5 4 3 1 10 1 10 1 10 1 10 Cout
- 13. Setting a Target Impedance R3 2.5 Setting a target impedance of 250mΩ results 4 4 in both output capacitance and ESR values for Lo Rs L2 A stable solution with the target impedance 5.5u 0.1 64n V2 1 4 4 2 2 v2 Cout I1 126u AC = 1 Lo Zout 1.2 180m Co ut 3 ESR Lo 140m 91m Cout 1.44 2 Zout v2 in volts Plot1 100m 2 1 vdb2 4 Cout 1.267 10 60.0m 15.0 20.0m 1 50.0u 150u 250u 350u 450u time in seconds 5.00 vdb2 in db(volts) x = 6.00kHz, y = -12.1 db(Ohms)=0.25 Ohms Lo Plot1 Rs Rp Co ut Lo Rp Co ut -5.00 Co ut ESR Rp Co ut -15.0 ESR 0.091 -25.0 10 100 1k 10k 100k 1Meg 10Meg frequency in hertz
- 14. Figures of Merit A regulator with a lower inductance value results in a lower capacitance for a given impedance while also operating with a wider range of ESR values LM317 vs our custom regulator at Iout=25mA 10 2 10 1 LM317 Custom 10 0 TR1 Rs=5 mΩ Rs=5 mΩ 10 -1 Rp=10 Ω Rp=2 Ω L=3.98 uH L=0.08 uH 10 -2 10 -3 102 103 104 105 106 107 f/Hz TR1: Mag(Gain) TR1(Memory): Mag(Gain)
- 15. Comparing Solutions Zout 0.1 A lower inductance device requires Lo Zout 1.2 Rp less capacitance than a higher Co ut 10 Inductance for a given target Lo Cout 1.44 Impedance value Zout 2 Lo Rs 3.98u 5m V2 Lo 1 4 Rs Rp Co ut Lo Rp Co ut Cout Co ut I1 ESR 573u AC = 1 Rp Co ut 3 ESR Rp 78m 2 Lo Rs 0.08u 5m V2 1 4 Cout LM317 Custom 11.5u I1 AC = 1 4 5 Cout 5.731 10 Cout 1.152 10 3 ESR 0.078 ESR 0.075 ESR 75m
- 16. Comparing Solutions 2 vdb2 3 vdb2#1 -10.0 While the lower inductance device LM317 Custom offers much faster response times -20.0 vdb2#1, vdb2 in db(volts) 2 3 Plot1 -30.0 -40.0 4 v2 5 v2#a -50.0 80.0m 10 100 1k 10k 100k 1Meg 10Meg frequency in hertz v2#a, v2 in volts 60.0m LM317 Plot1 40.0m For a given load capacitance, the ESR Custom required is related to the square root 20.0m of the inductance 5 0 4 20.0u 60.0u 100u 140u 180u time in seconds
- 17. ESR Controls Stability AND Impedance 5 vdb2 8 vdb2#5 9 vdb2#6 -10.0 5 vdb2, vdb2#5, vdb2#6 in db(volts) -20.0 9 8 Plot1 -30.0 Custom regulator using -40.0 11.5uF capacitor with ESR=75mΩ, 100mΩ and -50.0 150mΩ 1k 10k 100k 1Meg 10Meg frequency in hertz
- 18. A Corrollary For a given load capacitance, the ESR This application is at required is related to the square root 100mA, powering an SMD clock. of the inductance. The lower The LM317 has an inductance of inductance regulator is generally 2.8uH, calculated from either much more stable over a wider range the impedance or the resonant of conditions frequency with the capacitor 10 0 The high frequency inductance is 65nH from the interconnects TR1 10 -1 LM317 and custom 2500uF would be regulator with 10uF required ceramic capacitor For the LM317 to 102 103 104 105 106 107 match the f/Hz TR1: Mag(Gain) TR1(Memory): Mag(Gain) Custom regulator