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comparing CS and Cascode frequency response

Discussion in 'Electronic Basics' started by Matteo, May 2, 2007.

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  1. Matteo

    Matteo Guest

    hi all,
    I calculated the frequency response of the CS and Cascode amplifiers
    using the time constants method. Here they are:

    CS

    f = ( 2*PI*( Rs*Cgs + Rs*Cgs*(1+Av) + Rd*(Cdb+Cl)) )-1


    Cascode

    f = ( 2*PI*(Rs*Cgs1 + Cds1*2*Rs + Rd*(Cgd2+Cdb2*Cl) + 1/gm2*(Cdb1+Cgs2) )-1

    where:

    Rs = resistance of the imput signal
    Rd = resistance under Vdd
    Cl = load capacity

    Vdd
    |
    Rd
    |----------o Vout
    --- |
    Vcost--|| =
    --> |
    | ground
    |
    ---
    ----||
    | -->
    Rs |
    | |
    Vin ground
    |
    ground


    I calculated f using

    Rs = 50ohm
    Rd = 600ohm
    W = 592 micron

    and I obtained

    CS => f = 1.98EE+08
    Cascode => 2.08EE+08

    and I think that's a really little difference! where did I make the mistake?

    thank you very much!
     
  2. The Phantom

    The Phantom Guest

    You should show your work as you did in your earlier posts.
     
  3. Matteo

    Matteo Guest

  4. The Phantom

    The Phantom Guest

    When you say "frequency response", I would have thought you meant the
    transfer function, but apparently you mean the corner frequency, or the 3
    dB down frequency. Could you clarify this point?
     
  5. Matteo

    Matteo Guest

    The Phantom ha scritto:
    Sorry, f is the 3 dB cut-off frequency
     
  6. The Phantom

    The Phantom Guest

    Matteo,
    I will try to derive the transfer function of the cascode, and compute the
    3 dB frequency from that. The transfer function of the CS was derived by
    both you and me in another posting. I will use that to compute the 3 dB
    frequency of the CS configuration.

    If you want actual numbers, you will have to give me values of the
    following:

    gm1
    Cgs1
    Cdg1
    Cds1
    gm2
    Cgs2
    Cdg2
    Cds2

    and anything else I might need.
     
  7. Matteo

    Matteo Guest

    The Phantom ha scritto:
    but do you think that the time constants method brings to a wrong
    result? shouldn't it be correct?
    the current in M1 and M2 is the same

    using W = 592 micron
    Cgs1 = Cgs2 = 635 fF
    Cgd1 = Cgd2 = 124fF
    Cdb1 = Cdb2 = 770fF

    Id=3mA and Vov = 0.15 V
    gm1 = gm2 = 0.04 S

    thanks a lot! your help is very appreciated
     
  8. The Phantom

    The Phantom Guest

    I don't know this method, and rather than learn it, I will compute the 3
    dB down frequency by another method, which will provide a check.
     
  9. Matteo

    Matteo Guest

    The Phantom ha scritto:
    Thank you phantom, I'll wait for your results to check my work!
     
  10. The Phantom

    The Phantom Guest

    Matteo,

    1. In this pdf:
    http://www.thebags.it/listing/uni/Cascode_Configuration_Small_Signal.PDF

    you have Cds2 connected at the output. Shouldn't it be connected in
    parallel with Ro1; that is, across the gm2*Vgs2 source?

    2. Also, I need to know what values you used for Ro1 and Ro2.

    3. In the earlier schematic of the CS amplifier, you have an Rd value of
    4.7 ohms. The cascode has an Rd of 600 ohms. Are you using 600 ohms in
    both amplifiers for this most recent calculation?

    4. Are you expecting a large difference in the 3dB frequencies? I derived
    the transfer function for the cascode, and when I plot it versus frequency
    up to 1 GHz, I find the roll-off is dominated by the 600 ohm Rd and the 250
    pF output capacitance. The amplifier parasitics don't matter much in
    either amplifier. I don't have Ro1 and Ro2 in the derivation, so when you
    give me those values, I'll put them in and see if they make much
    difference.

    I'm getting values of around 200 MHz for the frequency at which the voltage
    output is down by half for both amplifiers. Perhaps the missing Ro1 and
    Ro2 may make a difference, but I don't think it will change by very much.
     
  11. Matteo

    Matteo Guest

    The Phantom ha scritto:
    Cds2=Cdb2 goes from the drain terminal to the grounding, therefore I
    think it's correct. I also checked it on a book..
    Ro1 = Ro2 = 2500 ohm
    because Id=2.5mA and LAMBDA=0.16
    yes, I'm using 600 ohms in both amplifiers for this calculation
    I already put Ro1 in my derivation but it doesn't appear in the 3db
    frequency; I think that Ro2 shouldn't make the difference because it's
    in parallel with Rd that is very little!
    I found the same results! but I read everywhere that the cascode
    configuration is really better thant the CS's one! where can I find this
    "better"? I really don't understand..

    thanks phantom
     
  12. Isn't Cds2 the capacitance from the drain to the source? That's why it is
    designated Cds, the ds meaning drain to source, not drain to ground. It would
    go from the drain to ground only if the source were grounded. There is of
    course a capacitance due to the package which is from drain to ground, but Cds
    is internal to the chip, and goes from drain to source.

    Since in the cascode, the source of the second FET isn't grounded, I think you
    need to connect it across the second current source which represents the effect
    of the second FET.

    It doesn't have much effect connected the way you have it because it is
    completely dominated by the 250 pF output capacitance. But, if it is connected
    across Ro2, then it will have an effect, expecially if the 250 pF is removed.
    I'll run some more simulations and report on the results.
    I will add Ro1 and Ro2 to the circuit and run the simulation again. Then I
    will remove the 250 pF output load and compare the performance of the two
    circuits. Perhaps then, without the 250 pF load, the cascode is better than the
    CS.
    Are you in Italy? I guess it's Sunday there. I am a night person, and I'll be
    up for a few more hours. I'll probably be able to do this in the next hour or
    so.
     
  13. Matteo

    Matteo Guest

    Rodger Rosenbaum ha scritto:
    Ok sorry, I didn't tell you that the *only* capacitance I'm going to put
    in my work are Cgd, Cgs and Cdb and NOT Cds.

    take a look here at page 15:
    http://www.thebags.it/listing/uni/lecture25annotat.pdf

    ( When I wrote Cdb2=Cds2 I meant (sorry) that I'll not consider Cds2 but
    only Cdb2. However I think (if I had used it) that Cdb2 should have gone
    in parallel with Cds2 because the source of the second MOS is connected
    to the ground and the bulk too )
    I think that the source of the second mosfet (the upper one) is grounded
    because the source is connected to a costant voltage generator => in the
    small signal model is grounded. I checked it in some diapos I found in
    the web.
    This'll be very interesting ..I would have done it if I had had a simulator!
    yes I'm in Italy! it 11 in the morning here. yuor help is very
    appreciated! ..I'm only trying to understand why my cascode doesn't go
    better than the CS ;)
     
  14. Look carefully at the PDF you gave above. The source of the second FET is not
    at AC ground; there is a current source connected between the source and the
    constant voltage generator labeled Vss. Current sources have high impedance.
    The gate of the second FET is connected to a voltage source, not a current
    source. Therefore, the gate of the second FET is at RF (AC) ground. If the
    source of the second FET were also at RF ground, then the second FET wouldn't
    have any gain because both the gate and source would be grounded.
    In the earlier post where I said that I go corner frequencies of about 200
    MHz, I had used a value of Rd of 4.7 ohms for both amplifiers.

    Now that I have used 600 ohms for Rd in both amplifiers, and with 250 pF
    connected at the output, I get a corner frequency of 2.25 MHz for both
    amplifiers. The frequency response is totally dominated by the 600 ohm and 250
    pF combination. I notice that your book doesn't show a large capacitor like 250
    pF on the output of the cascode.

    In order to get a large bandwidth, it is necessary to remove the 250 pF
    capacitor on the output. When I do this, I get a corner frequency of about 490
    MHz for the CS amplifier and about 504 MHz for the cascode.

    The purpose of a cascode is to eliminate the Miller effect reduction of
    bandwidth. If I reduce Cgd to zero, I see only a small effect in the
    simulation. I think that your FET has such a low Cgd (124 fF) that the Miller
    effect is almost negligible even in the CS amplifier, so that the cascode
    doesn't show much improvement.

    I'll do some more simulations tomorrow.
     
  15. Matteo

    Matteo Guest

    Rodger Rosenbaum ha scritto:
    I think I could not put Rd = 4.7 ohm because I want Vout = 1.8 volt in
    order to have a large swing.
    Vdd = RdId + Vout
    Id = 1.5/Rd
    choosing Rd=4.7 ohm means Id=319mA ..too much! 600ohm is better ;)
    I tried to remove my 250fF capacitance but the frequency is the same..
    in the cascode I
    used Rd=600 Id=3.1mA W=592micron and Vov=0.15
    why do you get a different value?
    yes, that's the central point ..I think you are right ..the miller
    effect is completely negligible
    because of Rd and 250fF at Vout
     
  16. I think I have misread your schematic. I read Cl as *250 pF*, but it appears
    that it is actually 250 fF. Is this correct? I thought your script character
    was a "p" when it's actually a "f". It might be a good idea to print. :)

    With this change, I now get a corner frequency of 315 MHz for the CS
    amplifier, and a corner frequency of 984 MHz for the cascode.
    By the way, I decided to double check your calculations from your original post:

    hi all,
    I calculated the frequency response of the CS and Cascode amplifiers
    using the time constants method. Here they are:

    CS

    f = ( 2*PI*( Rs*Cgs + Rs*Cgs*(1+Av) + Rd*(Cdb+Cl)) )-1


    Cascode

    f = ( 2*PI*(Rs*Cgs1 + Cds1*2*Rs + Rd*(Cgd2+Cdb2*Cl) + 1/gm2*(Cdb1+Cgs2) )-1

    and I obtained

    CS => f = 1.98EE+08 <<<For this one, I get 1.107E+08
    Cascode => 2.08EE+08 <<<For this one, I get 7.2915E+08

    You might want to check your calculations again.
     
  17. Matteo

    Matteo Guest

    Rodger Rosenbaum ha scritto:
    ehmm ..yes, sorry for my script character :p

    Wow .. but ..Can you tell me which values of W, Vov=Vgs-Vth, Rd and Rs
    did you used in this calculation please?
    thank you again
     
  18. I'm just using these values that you gave me:

    "the current in M1 and M2 is the same

    using W = 592 micron
    Cgs1 = Cgs2 = 635 fF
    Cgd1 = Cgd2 = 124fF
    Cdb1 = Cdb2 = 770fF
    Cl = 250 fF

    Id=3mA and Vov = 0.15 V
    gm1 = gm2 = 0.04 S"

    and:

    "Ro1 = Ro2 = 2500 ohm
    because Id=2.5mA and LAMBDA=0.16
    yes, I'm using 600 ohms in both amplifiers for this calculation"

    W doesn't appear in the expressions you gave for f, I use the various
    capacitances you gave me, and Rs = 50, Rd = 600, Av = 24.
     
  19. Matteo

    Matteo Guest

    Rodger Rosenbaum ha scritto:
    it's driving me mad.. I checked my calculations hundreds time and I
    always get the same values I posted days ago..

    for the cascode I put in my calculator:

    f = 1 / 2 / 3.14 / (50*635EE-15 + 124EE-15*2*50 + 600*(124EE-15 +
    770EE-15 + 250EE-15) + 1/0.04*(635EE-15 + 770EE-15)) = 207804859.6 =
    2.08EE+8 instead of your 7.2EE+8

    am I stupid? where am I making the mistake? #|
     
  20. I see two differences compared to the expression in your original post.
    should be 770EE-15
    About the first difference: in your posted expression you have Cds1; I used the
    value for Cdb1 for that.

    The second difference is * instead of +. Maybe it should really be +, but in
    the expression you posted it's *.
     
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