LM7805 Analysis and Simulation¶

By Shuo Chen (chenshuo_at_chenshuo.com)

Latest notebook: https://github.com/chenshuo/notes/blob/master/notebooks/LM7805.ipynb

Comments and discussions: https://github.com/chenshuo/notes/discussions

Series of analysis & simulation of IC regulator designed in 1970s:

μA78L05
LM7805 <- This page
TL431

LM7805 != μA7805¶

https://www.righto.com/2014/09/reverse-engineering-counterfeit-7805.html

In most if not all practices, LM7805 and μA7805 can be used interchangeablly, but their internal schematic are different. Ken Shirriff suspects "manufacturers are constrained by patents, so they use the part numbers they want on the devices they can make."

Two common designs:

LM7805 $=$ LM340 from National semiconductor. based on LM109/LM309 by Robert Widlar in 1969.
μA7805 from Fairchild semiconductor, debut in 1971.

$\newcommand{\uv}[1]{V_\mathrm{#1}}\newcommand{\ui}[1]{I_\mathrm{#1}}$The obvious difference is their reference voltage, μA7805 has 4 $\uv{BE}$ on its reference voltage, after temperature compensation $\uv{REF} \approx 4 \times V_\mathrm{g0}\approx 4.8$V. While LM7805 has 3 $V_\mathrm{BE}$ on its reference voltage, so after temperature compensation $\uv{REF} \approx 3 \times V_\mathrm{g0}\approx 3.6$V.

LM7805¶

Alias of LM340.

No description has been provided for this image

This is a vector graphic, right click and open it in a new tab, then zoom in as you need.

μA7805¶

The current TI datasheet doesn't specify resistor values, check 1971 Fairchild Linear Integrated Circuits Data Catalog instead.

A few notes:

Unlabelled $R_{21}$ between base of $Q_{15}$ and emitter of $Q_{16}$ didn't exist in 1971 or 1973 datasheets from Fairchild. So it's drawn in dashed lines.
Value of $R_{16}$ changes between 2kΩ and 6kΩ in different versions of datasheets, the value probably doesn't matter too much though.
$R_{20}=250$Ω is for 5V output, from this we can estimate the interal reference voltage at base of $Q_6$ is $\dfrac{5}{5+0.25}\times 5.0 = 4.762$V.
$Q_{16}$ and $Q_{17}$ is Darlinton pair, as the output stage, a.k.a. series pass transistors.
$Q_{15}$ and current sense resistor $R_{11}$ limits the output current. When in normal operation, $Q_{15}$ is off.
Zener diode $D_2$ and $Q_{15}$ prevent overvoltage break down of output pass transistors. (It's called "Output Transistor Safe-Area Compensation" in the datasheet.)
Zener diode $D_1$ and $Q_{14}$ provides overheat protection (called "Thermal-Overload Protection" in the datasheet). When in normal operation, $Q_{14}$ is off.
Zener diode $D_1$ and $Q_{12}$/$Q_{13}$ is startup circuit, provide initial bias for $Q_1, Q_7, Q_8$ when power up. When in normal operation, $Q_{13}$ is off.
The rest transistors $Q_1 \dots Q_{11}$ are the core function of voltage reference, error amplifier ($Q_4$, $Q_3$ and $Q_{11}$), current mirror ($Q_8$ and $Q_9$) as active load, etc.

μA7805¶

Simplified schematic¶

Adapted from 1974 Fairchild Voltage Regulator Applications Handbook, p.2-4

Brief analysis:

The main part of the bandgap reference: $Q_1$, $Q_2$ generates $\Delta V_\mathrm{BE}$ on $R_3$, and magnify it on $R_2$. $R_2$ is critical, as the voltage on it $V_\mathrm{R2}$ has positive tempco, to cancel negative tempco of 4 $V_\mathrm{BE}$s.

7805 works in a different way than μA78L05, the latter is traditional: generating stable reference voltage usng bandgap circuit, then comparing output voltage against it.

In 7805, the bandgap reference works "backwards", the whole chip can be viewed as a bandgap reference. The "purpose" of the circuit, including its external load, is maintaining a stable voltage at the base of $Q_6$, which according to literature, it is supposed to be 4.8V, that is $4 \times V_\mathrm{g0}$. What we really want from this circuit, is its "side-effect" of delivering stable 5V voltage output at Vout pin. In other words, the error amplifier made of $Q_3, Q_4, \mathrm{and} Q_{11}$, and the output pass transistors $Q_{16}$ and $Q_{17}$ are all part of the feedback look of the bandgap reference, whose error singal is from collector of $Q_2$.

$Q_4$ and $Q_3$ form a Darlinton pair to amplify the voltage error. I guess the initial design consists $Q_1, Q_2, Q_3$ only, $Q_4$ was added later to increase the gain of error amplifier. With the addition of $Q_4$, the voltage at collector of $Q_2$ increased to 2 $V_\mathrm{BE}$s, to compensate that, $Q_7$ was added to increase the voltage of Q1C to 2 $V_\mathrm{BE}$s as well. Then $R_{10}$ was added (not shown in the simplified schematic) to provide a path for emitter current of $Q_7$ (~132μA). The purpose was to keep the voltage drop on $R_1$ and $R_2$ the same, so that the current ratio on $Q_1$ and $Q_2$ is about $20:1$, 1420μA vs. 75μA.

Feedback loop:

$Q_6$ and $Q_5$ are emitter followers, $Q_4$ and $Q_3$ are error ampifier, those 4 transistors provides the negative tempco of voltage reference. Canceled by positive tempco on $V_\mathrm{R2}$
$Q_{11}$ (shown as dashed line in the simplified schematic) is a buffer, also a current amplifier, to minimize/reduce the current changes on $Q_4$ and $Q_3$, bacause $Q_4$ and $Q_3$ also serve as part of the bandgap voltage reference, we want their current stable.
Suppose load reduced, Vout ↑, Vref ↑, $V_\mathrm{Q6B}$↑, $V_\mathrm{Q5E}$↑, $V_\mathrm{Q4B}$↑, so the error voltage↑
$V_\mathrm{Q4B}$↑, $I_\mathrm{C4}$ and $I_\mathrm{C3}$ ↑↑, $I_\mathrm{E11}$ ↑↑↑, so $I_\mathrm{B16}$↓, (as $I_\mathrm{E11}+I_\mathrm{B16}+I_\mathrm{R16} = I_\mathrm{C9}$, and $I_\mathrm{C9}$ doesn't change much.)
$I_\mathrm{B16}$↓, $I_\mathrm{E16}$↓, $I_\mathrm{B17}$↓, $I_\mathrm{E17}$↓↓, Iout↓↓, finally Vout ↓.

Estimating quiescent operating point:

Assuming all $V_\mathrm{BE}\approx 0.65$V.
$V_\mathrm{Q1B} = V_\mathrm{Q3B} =0.65$V, $V_\mathrm{Q7B} = V_\mathrm{Q4B} =1.3$V
$V_\mathrm{R1} = V_\mathrm{R2}\ \Rightarrow\ I_\mathrm{R1} \cdot R_1 = I_\mathrm{R2} \cdot R_2$
$I_\mathrm{R1} = \dfrac{R_2}{R_1}I_\mathrm{R2} = 20 I_\mathrm{R2}$
$I_\mathrm{R1} \approx I_\mathrm{C1}$, $I_\mathrm{R2} \approx I_\mathrm{C2}$, so $I_\mathrm{C1} \approx 20 I_\mathrm{C2}$
$V_\mathrm{R3} = \Delta V_\mathrm{BE} = V_\mathrm{BE1} - V_\mathrm{BE2} = V_\mathrm{T} \ln \dfrac{I_\mathrm{C1}}{I_\mathrm{C2}}$
$\Delta V_\mathrm{BE} = V_\mathrm{T} \ln 20 \approx 3 V_\mathrm{T} = 77.3$mV
$V_\mathrm{R2} = \dfrac{R_2}{R_3} \Delta V_\mathrm{BE} = 20 \Delta V_\mathrm{BE} \approx 1.546$V
$V_\mathrm{Q5E} = V_\mathrm{R2} + V_\mathrm{Q4B} \approx 1.55 + 1.30 = 2.85$V
$V_\mathrm{REF} = V_\mathrm{Q6B} = V_\mathrm{Q5E} + V_\mathrm{BE5} + V_\mathrm{BE6} \approx 4.15$V

SPICE model¶

I couldn't find a SPICE model, so I made my own for helping analysis.

  * UA7805 DC path model
  V1    vin  0   10V
  Rload out  0   100

  * Bandgap reference
  R1  q5e  q1c      1k
  Q1  q1c  q1b 0    NPN
  Q7  q5e  q1c q1b  NPN
  R10 q1b  0        6k
  Q2  q4b  q1b r3   NPN
  R3  r3   0        1k
  R2  q5e  q4b      20k

  * Error amplifier
  Q4  q11b q4b  q3b  NPN
  Q3  q11b q3b  0    NPN
  R14 q3b  0         6k
  Q11 0    q11b q9c  PNP
  R16 q9c  q11b      6k

  * Current mirror
  R8  vin  q8e 100
  R9  vin  q9e 100
  Q8  q8b  q8b q8e  PNP
  Q9  q9c  q8b q9e  PNP

  * Feedback
  Q10 q8b  out q10e NPN
  Q5  q10e q6e q5e  NPN
  Q6  out  ref q6e  NPN
  R15 q6e  q5e      6k
  R19 ref  0        5k
  R20 out  ref      1.25k

  * Output
  Q16 vin  q9c  q17b NPN
  Q17 vin  q17b q17e NPN 10
  R11 q17e out       0.3
  R17 q17b out       200

  * Start-up
  R4  vin  q12b      100k
  D1  0    q12b      DZ
  R18 vin  q12c      500
  Q12 q12c q12b q12e NPN
  R5  q12e q13b      3.3k
  R6  q13b q14b      2.7k
  R7  q14b 0         500
  Q13 q8b  q13b q5e  NPN
  
  .MODEL NPN NPN( IS=5f BF=80  VAF=100 CJC=1P CJE=2P )
  .MODEL PNP PNP( IS=2f BF=60  VAF=50  CJC=1P CJE=2P )
  .MODEL DZ D(BV=5.6)

* .options savecurrents

This model doesn't have output current limiting or over voltage protection circuits.

   @d1[id] =   -36.01 uA
  @q10[ib] =    17.75 uA
  @q10[ic] =  1478.53 uA
  @q11[ib] =   -18.81 uA
  @q11[ic] = -1258.61 uA
  @q12[ib] =     8.85 uA
  @q12[ic] =   737.29 uA
  @q13[ib] =    -0.00 uA
  @q13[ic] =     0.00 uA
  @q16[ib] =    50.07 uA
  @q16[ic] =  4146.83 uA
  @q17[ib] =   565.04 uA
  @q17[ic] = 47118.99 uA
   @q1[ib] =    17.64 uA
   @q1[ic] =  1420.20 uA
   @q2[ib] =     0.93 uA
   @q2[ic] =    75.08 uA
   @q3[ib] =     0.45 uA
   @q3[ic] =    38.27 uA
   @q4[ib] =     1.16 uA
   @q4[ic] =    97.18 uA
   @q5[ib] =    18.53 uA
   @q5[ic] =  1496.29 uA
   @q6[ib] =     1.62 uA
   @q6[ic] =   130.78 uA
   @q7[ib] =     1.61 uA
   @q7[ic] =   130.63 uA
   @q8[ib] =   -23.86 uA
   @q8[ic] = -1431.82 uA
   @q9[ib] =   -22.85 uA
   @q9[ic] = -1444.12 uA
   @r10[i] =   113.66 uA
   @r11[i] = 47684.03 uA
   @r14[i] =    97.89 uA
   @r15[i] =   113.87 uA
   @r16[i] =   116.64 uA
   @r17[i] =  3631.85 uA
   @r18[i] =   737.29 uA
   @r19[i] =   805.44 uA
    @r1[i] =  1421.81 uA
   @r20[i] =   807.06 uA
    @r2[i] =    76.24 uA
    @r3[i] =    76.02 uA
    @r4[i] =    44.86 uA
    @r5[i] =   746.14 uA
    @r6[i] =   746.14 uA
    @r7[i] =   746.14 uA
    @r8[i] =  1455.69 uA
    @r9[i] =  1466.97 uA
 @rload[i] = 50360.29 uA
       out =  5036.03 mV
      q10e =  4353.91 mV
      q11b =  5771.47 mV
      q12b =  5514.02 mV
      q12c =  9631.36 mV
      q12e =  4849.91 mV
      q13b =  2387.65 mV
      q14b =   373.07 mV
      q17b =  5762.40 mV
      q17e =  5050.33 mV
       q1b =   681.96 mV
       q1c =  1301.99 mV
       q3b =   587.34 mV
       q4b =  1198.93 mV
       q5e =  2723.81 mV
       q6e =  3407.03 mV
       q8b =  9148.40 mV
       q8e =  9854.43 mV
       q9c =  6471.34 mV
       q9e =  9853.30 mV
        r3 =    76.02 mV
       ref =  4027.21 mV
 v1#branch = -54970.62 uA
       vin = 10000.00 mV

Copied!

print('Bias current = %.2f mA' % (54.971 - 50.36))
print('Bias current = %.2f mA' % (54.971 - 50.36))

Bias current = 4.61 mA

The following is the simulation result of DC operating point.

Line regulation¶

The datasheet says the typical $\Delta V_\mathrm{OUT}$ is 3mV when $V_\mathrm{IN}$ changing from 7V to 25V. Our model is 1.7mV.

.dc v1 7 25 0.1

Text(0.5, 1.0, 'Line regulation')

delta Vout = 1.69 mV, ratio 0.094 mV / V

Load regulation¶

The datasheet says the typical $\Delta V_\mathrm{OUT}$ is 15mV when $I_\mathrm{OUT}$ changing from 5mA to 1.5A. Our model is 7.6mV.

.dc rload 3 1000 1

Text(0.5, 1.0, 'Load regulation')

delta Vout = 7.58 mV, Output resistance 0.0045 Ohm

Startup circuit¶

quiescent current is too large, almost 1mA is wasted.

.dc v1 0 10 0.1

Text(0, 0.5, 'Vout (V)')

Vin = 6.00 V, Vout = 4.543 V, Dropout 1.46 V
Vin = 6.10 V, Vout = 4.638 V, Dropout 1.46 V
Vin = 6.20 V, Vout = 4.733 V, Dropout 1.47 V
Vin = 6.30 V, Vout = 4.827 V, Dropout 1.47 V
Vin = 6.40 V, Vout = 4.922 V, Dropout 1.48 V
Vin = 6.50 V, Vout = 5.000 V, Dropout 1.50 V
Vin = 6.60 V, Vout = 5.029 V, Dropout 1.57 V
Vin = 6.70 V, Vout = 5.037 V, Dropout 1.66 V
Vin = 6.80 V, Vout = 5.037 V, Dropout 1.76 V
Vin = 6.90 V, Vout = 5.037 V, Dropout 1.86 V
Vin = 7.00 V, Vout = 5.037 V, Dropout 1.96 V

Feedback¶

       @q10[ib]     17.756 uA,     17.712 uA, delta     -0.043 uA
       @q10[ic]   1478.852 uA,   1475.309 uA, delta     -3.542 uA
       @q10[ie]  -1496.607 uA,  -1493.022 uA, delta      3.586 uA
       @q11[ib]    -19.025 uA,    -16.310 uA, delta      2.715 uA
       @q11[ic]  -1271.141 uA,  -1099.414 uA, delta    171.727 uA
       @q11[ie]   1290.166 uA,   1115.724 uA, delta   -174.443 uA
       @q16[ib]     38.507 uA,    208.012 uA, delta    169.505 uA
       @q16[ic]   3192.112 uA,  17161.973 uA, delta  13969.861 uA
       @q16[ie]  -3230.619 uA, -17369.985 uA, delta -14139.367 uA
       @q17[ib]     33.088 uA,  11912.617 uA, delta  11879.529 uA
       @q17[ic]   2761.489 uA, 989954.471 uA, delta 987192.982 uA
       @q17[ie]  -2794.577 uA, -1001867.088 uA, delta -999072.511 uA
        @q1[ib]     17.647 uA,     17.603 uA, delta     -0.044 uA
        @q1[ic]   1420.520 uA,   1416.993 uA, delta     -3.527 uA
        @q1[ie]  -1438.167 uA,  -1434.596 uA, delta      3.571 uA
        @q2[ic]     75.086 uA,     75.038 uA, delta     -0.048 uA
        @q2[ie]    -76.020 uA,    -75.972 uA, delta      0.048 uA
        @q3[ib]      0.458 uA,      0.420 uA, delta     -0.038 uA
        @q3[ic]     38.501 uA,     35.513 uA, delta     -2.988 uA
        @q3[ie]    -38.959 uA,    -35.933 uA, delta      3.026 uA
        @q4[ib]      1.163 uA,      1.153 uA, delta     -0.010 uA
        @q4[ic]     97.215 uA,     96.819 uA, delta     -0.396 uA
        @q4[ie]    -98.378 uA,    -97.971 uA, delta      0.406 uA
        @q5[ib]     18.532 uA,     18.488 uA, delta     -0.044 uA
        @q5[ic]   1496.607 uA,   1493.022 uA, delta     -3.586 uA
        @q5[ie]  -1515.139 uA,  -1511.509 uA, delta      3.630 uA
        @q6[ic]    130.785 uA,    130.732 uA, delta     -0.054 uA
        @q6[ie]   -132.404 uA,   -132.349 uA, delta      0.055 uA
        @q7[ic]    130.632 uA,    130.577 uA, delta     -0.054 uA
        @q7[ie]   -132.242 uA,   -132.187 uA, delta      0.055 uA
        @q8[ib]    -23.869 uA,    -23.809 uA, delta      0.060 uA
        @q8[ic]  -1432.166 uA,  -1428.562 uA, delta      3.604 uA
        @q8[ie]   1456.035 uA,   1452.371 uA, delta     -3.664 uA
        @q9[ib]    -22.817 uA,    -22.939 uA, delta     -0.121 uA
        @q9[ic]  -1444.879 uA,  -1439.069 uA, delta      5.810 uA
        @q9[ie]   1467.696 uA,   1462.007 uA, delta     -5.689 uA
        @r10[i]    113.661 uA,    113.650 uA, delta     -0.011 uA
        @r11[i]   2794.577 uA, 1001867.087 uA, delta 999072.510 uA
        @r14[i]     97.920 uA,     97.551 uA, delta     -0.369 uA
        @r15[i]    113.872 uA,    113.862 uA, delta     -0.010 uA
        @r16[i]    116.695 uA,    116.031 uA, delta     -0.664 uA
        @r17[i]   3197.531 uA,   5457.368 uA, delta   2259.837 uA
        @r19[i]    805.507 uA,    804.772 uA, delta     -0.735 uA
         @r1[i]   1422.130 uA,   1418.602 uA, delta     -3.527 uA
        @r20[i]    807.125 uA,    806.390 uA, delta     -0.735 uA
         @r2[i]     76.249 uA,     76.191 uA, delta     -0.058 uA
         @r3[i]     76.020 uA,     75.972 uA, delta     -0.048 uA
         @r8[i]   1456.034 uA,   1452.371 uA, delta     -3.664 uA
         @r9[i]   1467.696 uA,   1462.007 uA, delta     -5.689 uA
      @rload[i]   5036.441 uA, 1006369.621 uA, delta 1001333.180 uA
            out   5036.441 mV,   5031.848 mV, delta     -4.593 mV
           q10e   4354.317 mV,   4349.787 mV, delta     -4.530 mV
           q11b   5677.925 mV,   6172.910 mV, delta    494.985 mV
           q12b   5514.025 mV,   5514.025 mV, delta     -0.000 mV
           q12c   9631.356 mV,   9631.356 mV, delta     -0.000 mV
           q12e   4849.905 mV,   4849.905 mV, delta     -0.000 mV
           q13b   2387.646 mV,   2387.646 mV, delta     -0.000 mV
           q14b    373.070 mV,    373.070 mV, delta     -0.000 mV
           q17b   5675.948 mV,   6123.322 mV, delta    447.374 mV
           q17e   5037.280 mV,   5332.408 mV, delta    295.129 mV
            q1b    681.965 mV,    681.901 mV, delta     -0.064 mV
            q1c   1302.001 mV,   1301.927 mV, delta     -0.074 mV
            q3b    587.518 mV,    585.306 mV, delta     -2.212 mV
            q4b   1199.144 mV,   1196.704 mV, delta     -2.440 mV
            q5e   2724.131 mV,   2720.530 mV, delta     -3.602 mV
            q6e   3407.362 mV,   3403.699 mV, delta     -3.663 mV
            q8b   9148.360 mV,   9148.792 mV, delta      0.432 mV
            q8e   9854.397 mV,   9854.763 mV, delta      0.366 mV
            q9c   6378.094 mV,   6869.097 mV, delta    491.002 mV
            q9e   9853.230 mV,   9853.799 mV, delta      0.569 mV
             r3     76.020 mV,     75.972 mV, delta     -0.048 mV
            ref   4027.535 mV,   4023.861 mV, delta     -3.674 mV
      v1#branch  -9659.479 uA, -1010812.969 uA, delta -1001153.490 uA
            vin  10000.000 mV,  10000.000 mV, delta      0.000 mV

Fixing tempco¶

0.33500589559324734

Changing $R_2$

R2 = 31 k, Vout@27C = 6.579 V, delta Vout =  167.9 mV
R2 = 30 k, Vout@27C = 6.433 V, delta Vout =  120.4 mV
R2 = 29 k, Vout@27C = 6.289 V, delta Vout =   73.1 mV
R2 = 28 k, Vout@27C = 6.145 V, delta Vout =   26.4 mV
R2 = 27 k, Vout@27C = 6.002 V, delta Vout =  -20.1 mV
R2 = 26 k, Vout@27C = 5.861 V, delta Vout =  -66.2 mV
R2 = 25 k, Vout@27C = 5.720 V, delta Vout = -112.0 mV
R2 = 24 k, Vout@27C = 5.581 V, delta Vout = -157.4 mV
R2 = 23 k, Vout@27C = 5.443 V, delta Vout = -202.4 mV
R2 = 22 k, Vout@27C = 5.306 V, delta Vout = -247.1 mV
R2 = 21 k, Vout@27C = 5.170 V, delta Vout = -291.2 mV
R2 = 20 k, Vout@27C = 5.036 V, delta Vout = -335.0 mV

<matplotlib.legend.Legend at 0x7f05fbb63a10>

Copied!





# R2 was 20k
r2 = 27
ng.cmd('alter r2 %d' % (r2*1000))
print_op()
# R2 was 20k
r2 = 27
ng.cmd('alter r2 %d' % (r2*1000))
print_op()

       out =  6002.43 mV
      q10e =  5309.48 mV
      q11b =  6736.01 mV
      q12b =  5514.02 mV
      q12c =  9631.36 mV
      q12e =  4849.91 mV
      q13b =  2387.65 mV
      q14b =   373.07 mV
      q17b =  6736.82 mV
      q17e =  6019.68 mV
       q1b =   692.90 mV
       q1c =  1314.85 mV
       q3b =   593.50 mV
       q4b =  1205.16 mV
       q5e =  3484.24 mV
       q6e =  4178.00 mV
       q8b =  9064.39 mV
       q8e =  9780.98 mV
       q9c =  7446.98 mV
       q9e =  9780.26 mV
        r3 =    84.28 mV
       ref =  4800.19 mV
 v1#branch = -66272.01 uA
       vin = 10000.00 mV

0.020429764616625157

Bring back the output voltage by adjusting $R_{20}$

Copied!





# R20 was 1.2k
ng.cmd('alter r20 230')
ng.cmd('dc temp 0 100 1')
temp = ng.vector('temp-sweep')
vout = ng.vector('out')
plt.plot(temp, vout)
print(max(vout) - min(vout))
# R20 was 1.2k
ng.cmd('alter r20 230')
ng.cmd('dc temp 0 100 1')
temp = ng.vector('temp-sweep')
vout = ng.vector('out')
plt.plot(temp, vout)
print(max(vout) - min(vout))

0.01647117642314555

Changing $V_\mathrm{BE}$?

Copied!





ng.circ('''
  V1    vin  0   10V
  Rload out  0   100

  * Bandgap reference
  R1  q5e  q1c      1k
  Q1  q1c  q1b 0    NPN
  Q7  q5e  q1c q1b  NPN
  R10 q1b  0        6k
  Q2  q4b  q1b r3   NPN
  R3  r3   0        1k
  R2  q5e  q4b      20k

  * Error amplifier
  Q4  q11b q4b  q3b  NPN 0.1
  Q3  q11b q3b  0    NPN 0.1
  R14 q3b  0         6k
  Q11 0    q11b q9c  PNP
  R16 q9c  q11b      6k

  * Current mirror
  R8  vin  q8e 100
  R9  vin  q9e 100
  Q8  q8b  q8b q8e  PNP
  Q9  q9c  q8b q9e  PNP

  * Feedback
  Q10 q8b  out q10e NPN
  Q5  q10e q6e q5e  NPN 0.1
  Q6  out  ref q6e  NPN 0.1
  R15 q6e  q5e      6k
  R19 ref  0        5k
  R20 out  ref      1.25k

  * Output
  Q16 vin  q9c  q17b NPN
  Q17 vin  q17b q17e NPN 10
  R11 q17e out       0.3
  R17 q17b out       200

  * Start-up
  R4  vin  q12b      100k
  D1  0    q12b      DZ
  R18 vin  q12c      500
  Q12 q12c q12b q12e NPN
  R5  q12e q13b      3.3k
  R6  q13b q14b      2.7k
  R7  q14b 0         500
  Q13 q8b  q13b q5e  NPN
  
  * .options savecurrents
.MODEL NPN NPN( IS=5f BF=80  VAF=100 CJC=1P CJE=2P )
.MODEL PNP PNP( IS=2f BF=60  VAF=50  CJC=1P CJE=2P )
.MODEL DZ D(BV=5.6)
''')


ng.cmd('dc temp 0 100 1')
temp = ng.vector('temp-sweep')
vout = ng.vector('out')
plt.plot(temp, vout, label='Area = 0.1')
print(max(vout) - min(vout))

ng.cmd('alter @q3[area] = 0.01')
ng.cmd('alter @q4[area] = 0.01')
ng.cmd('alter @q5[area] = 0.01')
ng.cmd('alter @q6[area] = 0.01')

# print_op()
ng.cmd('dc temp 0 100 1')
temp = ng.vector('temp-sweep')
vout = ng.vector('out')
plt.plot(temp, vout, label='Area = 0.01')
print(max(vout) - min(vout))
plt.legend()
ng.circ('''
  V1    vin  0   10V
  Rload out  0   100

  * Bandgap reference
  R1  q5e  q1c      1k
  Q1  q1c  q1b 0    NPN
  Q7  q5e  q1c q1b  NPN
  R10 q1b  0        6k
  Q2  q4b  q1b r3   NPN
  R3  r3   0        1k
  R2  q5e  q4b      20k

  * Error amplifier
  Q4  q11b q4b  q3b  NPN 0.1
  Q3  q11b q3b  0    NPN 0.1
  R14 q3b  0         6k
  Q11 0    q11b q9c  PNP
  R16 q9c  q11b      6k

  * Current mirror
  R8  vin  q8e 100
  R9  vin  q9e 100
  Q8  q8b  q8b q8e  PNP
  Q9  q9c  q8b q9e  PNP

  * Feedback
  Q10 q8b  out q10e NPN
  Q5  q10e q6e q5e  NPN 0.1
  Q6  out  ref q6e  NPN 0.1
  R15 q6e  q5e      6k
  R19 ref  0        5k
  R20 out  ref      1.25k

  * Output
  Q16 vin  q9c  q17b NPN
  Q17 vin  q17b q17e NPN 10
  R11 q17e out       0.3
  R17 q17b out       200

  * Start-up
  R4  vin  q12b      100k
  D1  0    q12b      DZ
  R18 vin  q12c      500
  Q12 q12c q12b q12e NPN
  R5  q12e q13b      3.3k
  R6  q13b q14b      2.7k
  R7  q14b 0         500
  Q13 q8b  q13b q5e  NPN
  
  * .options savecurrents
.MODEL NPN NPN( IS=5f BF=80  VAF=100 CJC=1P CJE=2P )
.MODEL PNP PNP( IS=2f BF=60  VAF=50  CJC=1P CJE=2P )
.MODEL DZ D(BV=5.6)
''')


ng.cmd('dc temp 0 100 1')
temp = ng.vector('temp-sweep')
vout = ng.vector('out')
plt.plot(temp, vout, label='Area = 0.1')
print(max(vout) - min(vout))

ng.cmd('alter @q3[area] = 0.01')
ng.cmd('alter @q4[area] = 0.01')
ng.cmd('alter @q5[area] = 0.01')
ng.cmd('alter @q6[area] = 0.01')

# print_op()
ng.cmd('dc temp 0 100 1')
temp = ng.vector('temp-sweep')
vout = ng.vector('out')
plt.plot(temp, vout, label='Area = 0.01')
print(max(vout) - min(vout))
plt.legend()

0.21101409673965943
0.09132583609916978

<matplotlib.legend.Legend at 0x7efe1a8a4f10>

LM7805¶

Simplified schematic¶

Estimating DC operating point, ignoring base currents (assuming $\beta \gg 1$).

R4 sets Ic2, R5 sets Ic4:

$\uv{R4} = \uv{B3} \approx \uv{R5} = \uv{B5}$, $\ui{R4}\,R_4\approx \ui{R5}\,R_5$
$\ui{R4}\approx\ui{E2}$, $\ui{R5}\approx\ui{E4}$, $\dfrac{\ui{E2}}{\ui{E4}} \approx\dfrac{R_5}{R_4} = 10.08$
$\uv{BE2}-\uv{BE4} = \uv{T}\ln \dfrac{\ui{E2}}{\ui{E4}} = \uv{T}\ln 10.08$

Similarly, R2 sets Ic3, R7 sets Ic5.

$\uv{R2} \approx \uv{R7}$, because their lower end is $2\uv{BE}$ from GND ($\uv{BE2}+\uv{BE3}\approx\uv{BE7}+\uv{BE8}$), higher end is $\uv{REF} - \uv{BE}$ ($\uv{BE1}\approx\uv{BE6}$)
$\ui{R2}\,R_2\approx \ui{R7}\,R_7$, while $\ui{R2}\approx\ui{C3}$ and $\ui{R7}\approx\ui{C5}$
$\dfrac{\ui{C3}}{\ui{C5}}=\dfrac{R_7}{R_2}=8.68$
$\uv{BE3}-\uv{BE5} = \uv{T}\ln \dfrac{\ui{E3}}{\ui{E5}} = \uv{T}\ln 8.68$

Voltage on R6 $\uv{R6} = \uv{BE2}+\uv{BE3} - \uv{BE4} - \uv{BE5} = \uv{T}\ln\dfrac{R_5\,R_7}{R_4\,R_2} = \uv{T}\ln 87.6\approx 115.4$mV

Voltage on R7 $\uv{R7} = \dfrac{R_7}{R_6}\uv{R6}=16.5\times\uv{R6}\approx 1.90$V

$\uv{REF}= \uv{B1}=\uv{B6} \approx \uv{R7}+3\uv{BE} = 1.90 + 3\times 0.65 = 3.85$V

SPICE model¶

https://github.com/kafana/ltspice-misc/blob/master/models/regulators.lib

Copied!





ng.circ('''
  V1 vcc 0 10
  Rload out 0 100
  X1 vcc 0 out LM7805
  .options savecurrents

.SUBCKT LM7805  Vin    GND    Out
* In GND Out
Q1          q1c   fb    q1e   Q_NPN 0.1
Q2          q1e   q2b   q3b   Q_NPN 0.1
Q3          q4b   q3b   GND   Q_NPN 0.1
C2          q3b   q4b         4p
R2          q1e   q2b         1.9K
R3          q2b   q4b         26
R4          q3b   GND         1.2K
R5          q5b   GND         12.1K
R6          q5e   GND         1K
R7          q6e   q7b         16.5K
R8          q9e   GND         4K
Q4          q6e   q4b   q5b   Q_NPN 0.1
Q5          q7b   q5b   q5e   Q_NPN 0.1
C1          q7b   q10b        20P
Q6          q16b  fb    q6e   Q_NPN 0.1
Q7          q10b  q7b   q8b   Q_NPN 0.1
Q8          q10b  q8b   GND   Q_NPN 0.1
Dq9         q8b   q9e  	      D_D 
Q10         GND   q10b  q10e  Q_PNP 0.1
R9          q10e  q10b        4K
R10         q15b  q10e        850
Q11         q11c  q11c  Vin   Q_PNP 0.1
Q11o        q15b  q11c  Vin   Q_PNP 0.1
Q12         Vin   q12b  q17b  Q_NPN 0.1
DZ1         GND   q12b        D_5V6
R1          Vin   q12b        80K
Q13         q15b  q13b  GND   Q_NPN 0.1
R13         q13b  GND         830
R11         q18b  q13b        4.97K
Q14         q15b  q14b  q14e  Q_NPN 1 
R14         q14b  q16e        380
R15         q14b  q16b        1.62K
R19         q14e  Out         100
DZ2         q14b  dz2k        D_5V1 
R17         Vin   dz2k        16K
Q15         Vin   q15b  q16b  Q_NPN 1
Q16         Vin   q16b  q16e  Q_NPN 10
R16         q16e  Out         250m
Q17         q11c  q17b  q1c   Q_NPN 0.1
Q18         q11c  q18b  q18e  Q_NPN 0.1
R12         q17b  q18b        7K
R18         q18e  q1e         500
R20         Out   fb          640
R21         fb    GND         2.67K

.MODEL D_5V1 D( IS=10F N=1.16 BV=5.1 IBV=0.5M CJ0 = 1P TT = 10p )
.MODEL D_5V6 D( IS=10F N=1.16 BV=5.6 IBV=5U CJ0 = 1P TT = 10p )
.MODEL Q_NPN NPN( IS=10F NF=1.16 NR=1.16 BF=80 CJC=1P CJE=2P TF=10P TR=1N )
.MODEL Q_PNP PNP( IS=10F NF=1.16 NR=1.16 BF=80 CJC=1P CJE=2P TF=10P TR=1N )
.MODEL D_D D( IS=1F N=1.16 CJ0 = 1P TT = 10p )

.ENDS LM7805
''')

x = print_op(1, 1)
ng.circ('''
  V1 vcc 0 10
  Rload out 0 100
  X1 vcc 0 out LM7805
  .options savecurrents

.SUBCKT LM7805  Vin    GND    Out
* In GND Out
Q1          q1c   fb    q1e   Q_NPN 0.1
Q2          q1e   q2b   q3b   Q_NPN 0.1
Q3          q4b   q3b   GND   Q_NPN 0.1
C2          q3b   q4b         4p
R2          q1e   q2b         1.9K
R3          q2b   q4b         26
R4          q3b   GND         1.2K
R5          q5b   GND         12.1K
R6          q5e   GND         1K
R7          q6e   q7b         16.5K
R8          q9e   GND         4K
Q4          q6e   q4b   q5b   Q_NPN 0.1
Q5          q7b   q5b   q5e   Q_NPN 0.1
C1          q7b   q10b        20P
Q6          q16b  fb    q6e   Q_NPN 0.1
Q7          q10b  q7b   q8b   Q_NPN 0.1
Q8          q10b  q8b   GND   Q_NPN 0.1
Dq9         q8b   q9e  	      D_D 
Q10         GND   q10b  q10e  Q_PNP 0.1
R9          q10e  q10b        4K
R10         q15b  q10e        850
Q11         q11c  q11c  Vin   Q_PNP 0.1
Q11o        q15b  q11c  Vin   Q_PNP 0.1
Q12         Vin   q12b  q17b  Q_NPN 0.1
DZ1         GND   q12b        D_5V6
R1          Vin   q12b        80K
Q13         q15b  q13b  GND   Q_NPN 0.1
R13         q13b  GND         830
R11         q18b  q13b        4.97K
Q14         q15b  q14b  q14e  Q_NPN 1 
R14         q14b  q16e        380
R15         q14b  q16b        1.62K
R19         q14e  Out         100
DZ2         q14b  dz2k        D_5V1 
R17         Vin   dz2k        16K
Q15         Vin   q15b  q16b  Q_NPN 1
Q16         Vin   q16b  q16e  Q_NPN 10
R16         q16e  Out         250m
Q17         q11c  q17b  q1c   Q_NPN 0.1
Q18         q11c  q18b  q18e  Q_NPN 0.1
R12         q17b  q18b        7K
R18         q18e  q1e         500
R20         Out   fb          640
R21         fb    GND         2.67K

.MODEL D_5V1 D( IS=10F N=1.16 BV=5.1 IBV=0.5M CJ0 = 1P TT = 10p )
.MODEL D_5V6 D( IS=10F N=1.16 BV=5.6 IBV=5U CJ0 = 1P TT = 10p )
.MODEL Q_NPN NPN( IS=10F NF=1.16 NR=1.16 BF=80 CJC=1P CJE=2P TF=10P TR=1N )
.MODEL Q_PNP PNP( IS=10F NF=1.16 NR=1.16 BF=80 CJC=1P CJE=2P TF=10P TR=1N )
.MODEL D_D D( IS=1F N=1.16 CJ0 = 1P TT = 10p )

.ENDS LM7805
''')

x = print_op(1, 1)

@c.x1.c1[i] =     0.00 uA
@c.x1.c2[i] =     0.00 uA
@d.x1.dq9[id] =    18.12 uA
@d.x1.dz1[id] =   -49.22 uA
@d.x1.dz2[id] =    -0.06 uA
@q.x1.q10[ib] =   -14.86 uA
@q.x1.q10[ic] = -1188.51 uA
@q.x1.q10[ie] =  1203.37 uA
@q.x1.q11[ib] =   -17.84 uA
@q.x1.q11[ic] = -1426.88 uA
@q.x1.q11[ie] =  1444.72 uA
@q.x1.q11o[ib] =   -17.84 uA
@q.x1.q11o[ic] = -1426.88 uA
@q.x1.q11o[ie] =  1444.72 uA
@q.x1.q12[ib] =     4.92 uA
@q.x1.q12[ic] =   393.64 uA
@q.x1.q12[ie] =  -398.56 uA
@q.x1.q13[ib] =    -0.00 uA
@q.x1.q13[ic] =     0.00 uA
@q.x1.q13[ie] =    -0.00 uA
@q.x1.q14[ib] =    -0.00 uA
@q.x1.q14[ic] =     0.00 uA
@q.x1.q14[ie] =    -0.00 uA
@q.x1.q15[ib] =    14.96 uA
@q.x1.q15[ic] =  1197.17 uA
@q.x1.q15[ie] = -1212.13 uA
@q.x1.q16[ib] =   631.50 uA
@q.x1.q16[ic] = 50520.31 uA
@q.x1.q16[ie] = -51151.81 uA
@q.x1.q17[ib] =    18.28 uA
@q.x1.q17[ic] =  1462.56 uA
@q.x1.q17[ie] = -1480.84 uA
@q.x1.q18[ib] =    -0.00 uA
@q.x1.q18[ic] =     0.00 uA
@q.x1.q18[ie] =    -0.00 uA
@q.x1.q1[ib] =    18.51 uA
@q.x1.q1[ic] =  1480.84 uA
@q.x1.q1[ie] = -1499.35 uA
@q.x1.q2[ib] =     8.59 uA
@q.x1.q2[ic] =   686.82 uA
@q.x1.q2[ie] =  -695.41 uA
@q.x1.q3[ib] =    10.04 uA
@q.x1.q3[ic] =   803.04 uA
@q.x1.q3[ie] =  -813.08 uA
@q.x1.q4[ib] =     0.90 uA
@q.x1.q4[ic] =    72.25 uA
@q.x1.q4[ie] =   -73.15 uA
@q.x1.q5[ib] =     1.33 uA
@q.x1.q5[ic] =   106.07 uA
@q.x1.q5[ie] =  -107.40 uA
@q.x1.q6[ib] =     2.20 uA
@q.x1.q6[ic] =   176.37 uA
@q.x1.q6[ie] =  -178.58 uA
@q.x1.q7[ib] =     0.26 uA
@q.x1.q7[ic] =    20.40 uA
@q.x1.q7[ie] =   -20.66 uA
@q.x1.q8[ib] =     2.54 uA
@q.x1.q8[ic] =   203.00 uA
@q.x1.q8[ie] =  -205.54 uA
@r.x1.r10[i] =  1411.92 uA
@r.x1.r11[i] =   380.28 uA
@r.x1.r12[i] =   380.28 uA
@r.x1.r13[i] =   380.28 uA
@r.x1.r14[i] =   404.32 uA
@r.x1.r15[i] =  -404.26 uA
@r.x1.r16[i] = 51556.13 uA
@r.x1.r17[i] =     0.06 uA
@r.x1.r18[i] =    -0.00 uA
@r.x1.r19[i] =     0.00 uA
@r.x1.r1[i] =    54.14 uA
@r.x1.r20[i] =  1528.13 uA
@r.x1.r21[i] =  1507.41 uA
@r.x1.r2[i] =   812.53 uA
@r.x1.r3[i] =   803.94 uA
@r.x1.r4[i] =   685.37 uA
@r.x1.r5[i] =    71.83 uA
@r.x1.r6[i] =   107.40 uA
@r.x1.r7[i] =   106.33 uA
@r.x1.r8[i] =    18.12 uA
@r.x1.r9[i] =   208.55 uA
 @rload[i] = 50028.00 uA
       out =  5002.80 mV
 v1#branch = -55054.76 uA
       vcc = 10000.00 mV
   x1.dz2k =  9999.02 mV
     x1.fb =  4024.80 mV
   x1.q10b =  4555.23 mV
   x1.q10e =  5389.43 mV
   x1.q11c =  9160.31 mV
   x1.q12b =  5668.61 mV
   x1.q13b =   315.63 mV
   x1.q14b =  5169.33 mV
   x1.q14e =  5002.80 mV
   x1.q15b =  6589.56 mV
   x1.q16b =  5824.22 mV
   x1.q16e =  5015.69 mV
   x1.q17b =  4867.57 mV
   x1.q18b =  2205.62 mV
   x1.q18e =  3184.00 mV
    x1.q1c =  4027.14 mV
    x1.q1e =  3184.00 mV
    x1.q2b =  1640.19 mV
    x1.q3b =   822.44 mV
    x1.q4b =  1619.29 mV
    x1.q5b =   869.10 mV
    x1.q5e =   107.40 mV
    x1.q6e =  3247.84 mV
    x1.q7b =  1493.43 mV
    x1.q8b =   781.18 mV
    x1.q9e =    72.49 mV

Quiescent current¶

Copied!

ng.cmd('alter rload 1k')
print_op()
ng.cmd('alter rload 1k')
print_op()

       out =  5002.84 mV
 v1#branch = -10036.89 uA
       vcc = 10000.00 mV
   x1.dz2k =  9997.95 mV
     x1.fb =  4024.83 mV
   x1.q10b =  4454.26 mV
   x1.q10e =  5288.64 mV
   x1.q11c =  9160.31 mV
   x1.q12b =  5668.61 mV
   x1.q13b =   315.63 mV
   x1.q14b =  5146.06 mV
   x1.q14e =  5002.84 mV
   x1.q15b =  6494.95 mV
   x1.q16b =  5749.49 mV
   x1.q16e =  5004.47 mV
   x1.q17b =  4867.57 mV
   x1.q18b =  2205.62 mV
   x1.q18e =  3184.02 mV
    x1.q1c =  4027.14 mV
    x1.q1e =  3184.02 mV
    x1.q2b =  1640.19 mV
    x1.q3b =   822.44 mV
    x1.q4b =  1619.29 mV
    x1.q5b =   869.10 mV
    x1.q5e =   107.40 mV
    x1.q6e =  3247.87 mV
    x1.q7b =  1493.46 mV
    x1.q8b =   781.20 mV
    x1.q9e =    72.50 mV

Copied!

print(10.03689 - 5.00284)
print(10.03689 - 5.00284)

5.03405

Input¶

Vin = 6.00V, Vout = 4.4677 V
Vin = 6.10V, Vout = 4.5664 V
Vin = 6.20V, Vout = 4.6651 V
Vin = 6.30V, Vout = 4.7637 V
Vin = 6.40V, Vout = 4.8619 V
Vin = 6.50V, Vout = 4.9580 V
Vin = 6.60V, Vout = 5.0014 V
Vin = 6.70V, Vout = 5.0029 V
Vin = 6.80V, Vout = 5.0029 V
Vin = 6.90V, Vout = 5.0028 V
Vin = 7.00V, Vout = 5.0028 V

Line regulation¶

0.01970506928827831

[<matplotlib.lines.Line2D at 0x7f2bead16f10>]

0.9663296921011977

[<matplotlib.lines.Line2D at 0x7f2beadf9a50>]

Load regulation¶

Copied!





ng.cmd('dc rload 3 1000 1')
rload = ng.vector('res-sweep')
vout = ng.vector('out')
iout = vout / rload
plt.plot(iout, vout)

delta =  (vout[-1] - vout[0])
print('delta Vout = %.2f mV, in %.4f Ohm' % (1e3 * delta, delta / (iout[0] - iout[-1])))
ng.cmd('dc rload 3 1000 1')
rload = ng.vector('res-sweep')
vout = ng.vector('out')
iout = vout / rload
plt.plot(iout, vout)

delta =  (vout[-1] - vout[0])
print('delta Vout = %.2f mV, in %.4f Ohm' % (1e3 * delta, delta / (iout[0] - iout[-1])))

delta Vout = 1.39 mV, in 0.0008 Ohm

Short-circuit¶

Copied!





ng.cmd('dc rload 0.1 5 0.1')
rload = ng.vector('res-sweep')
vout = ng.vector('out')
iout = vout / rload
plt.plot(iout, vout)

delta =  (vout[-1] - vout[0])
print(vout[0])
ng.cmd('dc rload 0.1 5 0.1')
rload = ng.vector('res-sweep')
vout = ng.vector('out')
iout = vout / rload
plt.plot(iout, vout)

delta =  (vout[-1] - vout[0])
print(vout[0])

0.1716012232593159

Tempco¶

Copied!





ng.cmd('dc temp 0 100 1')
plt.plot(ng.vector('temp-sweep'), ng.vector('out'))
print(max(ng.vector('out')) - min(ng.vector('out')))
print(119/150)
print(97.6 / 100)
ng.cmd('dc temp 0 100 1')
plt.plot(ng.vector('temp-sweep'), ng.vector('out'))
print(max(ng.vector('out')) - min(ng.vector('out')))
print(119/150)
print(97.6 / 100)

0.09759713480243715
0.7933333333333333
0.976