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A curious circuit

Discussion in 'Electronic Design' started by PN2222A, Nov 6, 2005.

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  1. PN2222A

    PN2222A Guest

    Posting a circuit I saw in EE Times lo these many years ago.

    current source

    5 mA

    | V1



    | |

    | |

    | |

    /=====/ >

    ^ 1K < 1K

    / \ >

    --- <

    | R? |


    | |
    < ^
    < ---

    | |

    | |

    ----- -----

    / / / / / /

    R? has an initial value of 1K ohms.

    Decrease it to 100 ohms.

    What happens to voltage V1 as the resistance decreases?

    I found it interesting.

  2. John - kd5yi

    John - kd5yi Guest

    It increases.

  3. Bob Monsen

    Bob Monsen Guest

    (I fixed your drawing, I think... You meant two zeners of 6.1V each,

    According to spice, the voltage peaks at about 220 ohms.

    There is a balancing act between the zeners and the resistors. When R is
    0 ohms, the voltage across the circuit is clearly 10V. As R increases, the
    voltage increases, that is, until the zener diodes start to conduct. That
    point is when 5mA * (1k+R) == 6.1V, ie, where R=220 ohms. After that, as R
    gets larger, more of the current flows directly through the zeners,
    bypassing R. So, the voltage decreases. When R is infinite, the voltage is
    6.1+(2.5mA * 1k) = 8.6V, since the current divides between the two

    Bob Monsen

    Mathematics is nothing more, nothing less, than the exact part of our
    - Luitzen Brouwer
  4. Luo XiaoZen

    Luo XiaoZen Guest

    Why did you find it interesting?
  5. PN2222A

    PN2222A Guest

    current source
    5 mA
    | V1
    | |
    | |
    | |
    /=====/ >
    ^ 6.2V < 1K
    / \ >
    --- <
    | R? |
    | |
    < ---
    | |
    | |
    ----- -----
    / / / / / /

    I found it interesting (as did the original article) because
    decreasing r? intuitively would seem to reduce the total
    resistance (or voltage drop) of the network.

    Imagine that instead of wires and components, this is a network
    of roadways with the particular kinds of traffic jams:
    Opening up a connector road within the roadways would not
    be expected to increase the driving delay -- more roads, less
    traffic ... (short term result only).

    But here, making a bypass road available increases the delay.

  6. I read in that PN2222A <>
    What is the road transport analogue of a zener diode? A traffic light at
    road works?
  7. Tim Williams

    Tim Williams Guest

    With nodes and wires labeled as shown, write all the immediately known
    [1] Io = (I1 + I2) = (I3 + I4) (parenthesis for emphasis)
    [2] I2 + I4 + I5 = 0
    [3] I1 + I3 + I5 = 0
    (Kirchoff's node rule)
    [4] V1 = V3 + 6.2 = (V1 - V2) + 6.2
    (loop rule; assuming zeners are forward-biased, a dangerous
    proposition at only 5mA)
    [6] I5 = (V3 - V2) / R
    [7] I1 = (V1 - V2) / R1
    [8] I4 = V3 / R2
    (Ohm's law)
    Now it's algebra.
    Add [2] + [3]:
    (I1 + I2) + (I3 + I4) + 2*I5 = 0 (parenthesis for emphasis)
    Transitive property with [1]:
    2*Io + 2*I5 = 0
    Substitute [6]:
    2*Io + 2*(V3 - V2) / R = 0 <divide by two--> Io = (V2 - V3) / R
    Take [4] and cancel the 6.2 volt terms:
    V3 = V1 - V2 --> V1 = -(V2 + V3) --> (V2 + V3) = -V1
    (Signs are whacky in this problem, better to keep them straight
    as we go, and figure it out later. The magnitudes are right.)
    Substitute modified [4] into our equation:
    Io = (-V1) / R --> - R * Io = V1.
    (The current obviously isn't in opposition to V1 nor is R negative, so I got
    something backwards in the problem. Again, only the quantity matters; sign
    is a point of view depending on which way your voltmeter probes are. ;-)

    ....Odd, when I did that on paper, I got V1 = Io * R * R1/R2, which of course
    comes out the same because R1 = R2 in the problem, but we haven't stated
    this fact -- see [7] and [8].

    If the zener diodes are not turned on, i.e., V1 - V3 < 6.2V and V2 < 6.2V,
    the problem becomes three resistors in series, and V1 = Io*(R1 + R + R2).

    Neither of these equations suggest a maxima with respect to R though, so
    something must be fishy.

  8. Jim Thompson

    Jim Thompson Guest

    You need to analyse it as two circuits based on breakpoints... zeners
    not conducting, or zeners conducting.

    Below ~255 ohms, the zeners aren't conducting.

    At zero ohms the voltage is (obviously) 10V.

    As the resistor increases you reach a peak of ~11.137V, and the zeners
    begin conduction.

    Any value above 255 ohms the voltage begins falling, being ~8.99V at

    ...Jim Thompson
  9. GPG

    GPG Guest

    With ideal components, by inspection the voltage across R will be 1.2v,
    R = 240O at break and the total 11.2v. With R infinite v = 8.7v
  10. GPG

    GPG Guest

    R =240, the ohms sign became a 0
  11. Jim Thompson

    Jim Thompson Guest

    Yep, I used a real 6.2V zener model and swept R.

    ...Jim Thompson
  12. Don Foreman

    Don Foreman Guest

    Equate voltage with delay time, current with traffic volume. The
    analog would be a road with ample capacity but speed limit so
    travel time is independent of traffic volume.
  13. I read in that Don Foreman
    <>) about 'A curious circuit',
    That's a delay line. I equated queue length with voltage (potential) and
    volume to current.
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