Linear Voltage Regulator
3-Terminal Adjustable
(LM317 Type)
While an Amplifier scales an input signal, the Regulator produces a fixed output, independent of the input signal (within a reasonable range)!
- How can you translate the datasheet's specs into output voltage errors?
- How does resistor tolerance impact the output error?
In this topic you'll get
- a step-by-step approach
- walk thru each error source
- derive the circuit and sensitivity equations
- an Excel file
- enter errors in a systematic format
- vary parameters, see their effect on total error
- customize & expand template for your own designs
For tutorials on Key Concepts and other circuits, goto EBA Series
OFFSET ERRORS
From the most general definition of an amplifier block, we'll see that the regulator can be defined by Offset Errors only!
- General Amplifier with ideal Gain (K) and Offset (Voffset).
- Vo = Vin*K + Voffset
- However, the Regulator produces a fixed voltage Voffset
only (no Gain applied to a varying input signal).
- Vo = Voffset
- The actual output with error (a change in offset from ideal)
- Vo = Voffset + ∆Voffset
For clarity we'll define the "input" to the regulator as
"vin_reg". While vin_reg provides a power source
for the regulator, we know it's NOT considered an input to be amplified.
MAX ERROR BUDGET
The max budget (target spec) for the regulator has been chosen as:
- Offset Error: ∆Voffset = 250mV
- Gain Error: Not Applicable (no input signal vin)
LINEAR REGULATOR
Schematic with Errors
Overview
The regulator produces an output voltage that can be described by.
- The internal Vref defines the golden reference that sets the output voltage.
- R1 and R2 create part of a feedback loop to servo a scaled version of Vref at the output vo.
- A small current Iref biases the internal Vref circuit. This current flows out the adjust pin creating an undesireable voltage through R2.
Device Errors
We'll analyze offset errors only for this topic.
| Description | Initial, Drift Error |
|---|---|
| OFFSET ERRORS | |
| U1, Vref, Internal Reference Voltage U1, Iref, Input Reference Current U1, ∆vo/∆vin_reg, Input Line Regulation U1, ∆vo/∆Io, Output Load Regulation R1, Resistor Tolerance R2. Resistor Tolerance |
50mV, 50uV/C 50uA, 2uA/C 0.03 V/V 0.02 V/A 0.1%, 100ppm/C 0.1%, 100ppm/C |
Conditions and Assumptions
Temperature
- Ambient: Ta = 25C
- Drift: ∆T = 30C
5V Regulator
- Vref = 1.25V, R1=1500, R2=499
- Vo = Vref*(R2/R1+1)=5.04V
Errors
- Errors calculated Referred to Input (RTO) at Vo.
- Errors totaled as WCA (Worst Case Analysis)
OFFSET ERRORS
Because the Regulator produces a fixed voltage (no Gain applied to a varying input signal), all errors will be categorized as Offset Errors.
REFERENCE VOLTAGE (Vref)
The regulator's output voltage can be described by
To calculate the Sensitivity of vo to Vref, we'll leverage a handy tool named superposition (set Iref=0) and solve for vo/vref.
Now, given an actual error (∆Vref = 200mV for example), the output error becomes
| Description | Initial Errors | Drift Errors |
| Error Source: e | ∆Vref = 50mV | ∆Vref _TC = 50uV/C |
| Pick Analysis Node: Va | vo | vo |
| Calc Sensitivity: S How does e impact Va? |
S = vo / vref = R2/R1+1 = 4.0 |
S = 4.0 |
| Calc Offset Error at Analysis Node Initial: ∆Voffset = e * S Drift: ∆Voffset = e * ∆T * S |
∆Voffset = 50mV * 4 = 200mV |
∆Voffset = 50uV/C * 30C * 4 = 1.5 mV |
| Calc Gain from Analysis Node to Output: Ka = Vo / Va | Ka = 1 | Ka = 1 |
| Calc Error RTO (Referred-to-Output): ∆voffset_RTO = ∆voffset * Ka |
∆voffset_RT0 = 200mV * 1 = 200mV |
∆voffset_RTI = 1.5mV / 5 = 0.3mV |
REFERENCE CURRENT (Iref)
The output voltage can be described by
To calculate the Sensitivity of vo to Iref, we'll again leverage superposition (set Vref=0) and solve for vo/Iref.
| Description | Initial Errors | Drift Errors |
| Error Source: e | ∆Iref = 50uA | ∆Iref _TC = 5uA/C |
| Pick Analysis Node: Va | vo | vo |
| Calc Sensitivity: S How does e impact Va? |
S = vo / iref = 1500 |
S = 1500 |
| Calc Offset Error at Analysis Node Initial: ∆Voffset = e * S Drift: ∆Voffset = e * ∆T * S |
∆Voffset = 50uA * 1500 = 20mV |
∆Voffset = 5uA/C * 30C * 1500 = 1.5 mV |
| Calc Gain from Analysis Node to Output: Ka = Vo / Va | Ka = 1 | Ka = 1 |
| Calc Error RTO (Referred-to-Output): ∆voffset_RTO = ∆voffset * Ka |
∆voffset_RT0 = 200mV * 1 = 200mV |
∆voffset_RTI = 1.5mV * 1 = 0.3mV |
RESISTOR (R1)
The output voltage is a function of R1
To calculate the Sensitivity, we'll increment R1 by a small amount to find how a change in R1 causes a change in vo.
Then, calculating S given a change in R1 (as a ratio) is simply
| Description | Initial Errors | Drift Errors |
| Error Source: e | R2_Tol = 0.1% |
R1_TC = 100ppm/C = 0.0001%/C |
| Pick Analysis Node: Va | vo | vo |
| Calc Sensitivity: S How does e impact Gain vo? Apply Difference Method: S = ∆vo / (∆R/R) |
vo=Vref*(R2/R1+1) +Iref*R2 vo'= Vref*(R2/(R1*1.01)+1) +Iref*R2 ∆vo=vo'-vo ∆R/R = 0.01 S = ∆vo / (∆R/R) = +4000 |
S = 0.5 |
| Calc Offset Error at Analysis Node Initial: ∆Voffset = e * S Drift: ∆Voffset = e * ∆T * S |
∆Voffset = 50uA * 1500 = 20mV |
∆Voffset = 5uA/C * 30C * 1500 = 1.5 mV |
| Calc Gain from Analysis Node to Output: Ka = Vo / Va | Ka = 1 | Ka = 1 |
| Calc Error RTO (Referred-to-Output): ∆voffset_RTO = ∆voffset*Ka |
∆voffset_RT0 = 200mV * 1 = 200mV |
∆voffset_RTI = 1.5mV * 1 = 0.3mV |
RESISTOR (R2)
The output voltage is a function of R2
To calculate the Sensitivity, we'll increment R2 by a small amount to find how a change in R2 causes a change in vo.
Then, calculating S given a change in R2 (as a ratio) is simply
SUMMARY
Let's review the Errors from the Offset Error sheet.
Description Initial Drift OFFSET ERRORS U1 Vref R1
R2
Total noise must be calculated using Root Sum Squares (RSS).
- RSS = √(∆Voffset12 + ∆Voffset22 + ...)
= 13.6 uVpk (4.53 uVrms)
Does the Total Noise Error (peak) fly under the Max Error Budget?
- RSS < 100 uVpk Yes - PASS!
NOISE VS. APP NOTE?
- The noise calculations were very similar to results in the App note!
- The App Note had a 1% lower noise. Why? It appears the App Note calculated the noise at the op amp's input, but omitted the final step of referring the noise to Vin. This omission under-estimates noise for inverting amplifiers. The impact is more noticable for lower gains.
- This method explicitly calculates noise at Vin.
EBA WITH EXCEL
An Excel file was created to implement the error budget analysis.
- Organizes complex analyses into smaller managable sections
- Easier to create, review and debug
- Customizable and expandable to more complex circuits
- Modular for reuse in other designs
3 Worksheets
Worksheet Enter Calculate CIRCUIT CALC Circuit values Signal gains, levels and error sensitivities (S) OFFSET Offset error sources Offset errors and totals GAIN Gain error sources Gain errors and totals
While 3 worksheets seems over-the-top for smaller circuits,
you'll find a big advantage when analyzing more complex circuits or
multi-stage systems!
Try the Excel file: amp1-noise.xlsx
Right Click on the filename, select "Save link as...".
- Open file, explore the Calc, Offset and Gain Sheets
- Hover over RED cornered cells for special noise calc notes!
- Play in the sandbox, modify values, see the impact on errors.
- Copy to a new file - experiment!
TRY IT!
- Increase all resistors by 10x (for a lower power design).
- What effect does this have on total noise?
- Suppose you're asked to try an op amp with 5x the input voltage noise (for a lower cost design).
- Does the amplfier design still meet spec?
REFERENCES
- Noise Calculations of Op-Amp Circuits, Application Note, Renesas Electronics.
- ISL28136, Precision, Rail-to-Rail, Op Amp Datasheet, Renesas Electronics.
- Tolerance Design of Electronic Circuits, Robert Spence, Randeep Soin, World Scientific Publishing.
For in-depth tutorials and more circuits, go to
EBA Series