Agilent How to Design T-Coils using Agilent Genesys Presented by: Allen Hollister Author of Wideband Amplifier Design textbook VP Engineering at: Besser Associate
To the wideband amplifier designer, the world looks like a low-pass filter with insufficient bandwidth Invariably, the load begins to look like a capacitor at some frequency Hopefully a pure capacitor without negative elements We will, in fact, work to make the load look purely capacitive. Where we cannot, we will attempt to use the additional elements to our advantage. Invariably, the source driving that load has some output impedance—hopefully resistive Again, we will work to make the output impedance look purely resistive Where we cannot, we will attempt to use the additional elements to our advantage. If successful in making the amplifier inputs look purely capacitive, the result is a single pole RC filter The bandwidth will be 1/(2 pi RC) Once we realize we have a LPF, we now make it a two pole filter by adding some additional elements that cause the filter to become MFED
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We Use Peaking Circuits to Get As Much Bandwidth as Possible
Peaking networks, which can be as simple as some series inductance or as complex as a T-Coil that contains mutual inductance, increase the bandwidth by some factor termed the Bandwidth Improvement Factor. This factor ranges from 36% to 272% for MFED filters
Depicted are Thevenin and Norton equivalents for an RC LPF. Both are useful in different circumstances. The bandwidth for these circuits is 1/(2 pi R1 C1) and the risetime is 2.2 R1 C1
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Assume that R1 = 50Ωand C1 = 1pF• Choose 1 pF because it is a
nice number for scaling• Choose 50 Ω because it is
This slide shows the theoretical bandwidth of the circuit. For a 50 Ohm source resistor and a 5 pF capacitive load, the theoretical bandwidth is 636.6 MHz and the risetime is 0.549 ns
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I1
L13
R1
C1 Vout
L23
Cb
M
Zin
1 2
3Ls=L13Lr=L23
If the values of Ls, Lr, M, and Cb are selected appropriately for the values of R1 and C1 then:
The Bandwidth Improvement Factor will be 2.72
The filter will be two pole and have an MFED step response
Zin will equal R1 for all frequencies (until the parts no longer look like R’s, L’s and C’s)
Can be used as a transmission line termination
Other kinds of filters (MFA, etc) can also be created with this same input impedance property
An advanced form of peaking termed T-Coil peaking because of its shape in the schematic is shown in the schematic. This technique requires the use of mutual inductance. With proper selection of values, this technique provides a bandwidth improvement factor of 2.72 while maintaining an MFED filter response. In addition, Zin is equal to R1 for all frequencies as long as the component elements remain close to ideal. This very useful property allows the device to be a transmission line termination. Well beyond the scope of this presentation is the ability of the T-Coil to provide, within limits, the same benefits shown here even if there is additional resistance and inductance in series with C1. Doing this requires that L13 differ from L23 creating what is known as an unbalanced T-Coil. For more information about unbalanced T-Coils see my book Wideband Amplifier Design or attend one of the seminars I put on in conjunction with Agilent. This circuit was first invented and patented by Carl Battajes of Tektronix (a mentor and close friend of mine) The properties of this circuit are so amazing that it, along with another of Carl’s inventions, the ft doubler made possible the high frequency scopes of the mid-60-s and 70-s. It is still a mainstay of these ultra-wideband amplifiers.
•After a lot of algebra (not shown in this webinar) we will find that if the values for Ls, Lr, and Cb are defined by the equations shown in the pink boxes, then the equations at the bottom of the page shown in green will be true!
Presenter
Presentation Notes
Shown in this slide and the next are the equations that define the T-Coil filter. The derivation of these equations are beyond the scope of this presentation. For an MFED filter, we will want k = 0.5 With k known, it is now possible to work out all the other required parameters (for a given R and C) to make the T-Coil work. The equations in yellow are definitions. The ones in orange are required T-Coil parameters. I show these without proof. Their derivation is straight forward, but tedious, and beyond the scope of this presentation. The equations in green are the resulting circuit equations. Observe that the transfer function from input to output, is now a two pole LPF. We will see later that we can set these poles to any desired position allowing us to create different kinds of filters. The transfer function, Vr/Iin represents an all-pass circuit where the output remains constant amplitude, but the phase changes at a critical frequency.
• Shown is a standard form for second order systems that we will use heavily
• This form will allow us to develop a generalized theory that can then be applied to specific circuits
• The damping factor δ, is a parameter that we will use heavily
Presenter
Presentation Notes
We are going to make heavy use of what is called a “standard form” for a second order system. Once we understand the parameters of this form we will be able to use the parameters to describe any two pole system no matter how it was generated. Delta determines the kind of LPF filter created. We will see shortly that if delta is SQRT(3)/2, (Theta is 30 degrees), the filter will be what we call Maximally Flat Envelop Delay and will have good step response. If delta is SQRT(2)/2 (Theta is 45 degrees), the filter becomes a Butterworth filter.
This exercise will allow us to derive the T-Coil parameters in terms of δ, R1, and C1
Presenter
Presentation Notes
Comparing the standard form to the previous RLC circuit, we can define the standard form parameters in terms of the RLC parameters (and vice versa) We begin by equating the term in front of S^2 on both equations; the standard from F(s) and the T-Coil LPF transfer function. This gives an equation for T in terms of the T-Coil parameters. Next we equate the terms in from of S for both equations and substitute in for T in order to solve for delta as a function of T-coil parameters. In fact, we find that delta is purely a function of the coefficient of coupling k. In fact we can now turn this around and solve for k as a function of delta. We see that k is completely determined by delta. Thus we now know one of the required T-Coil parameters (k) and we see that this parameter is set by the desired filter characteristic that is set by the damping factor delta.
The equations in the pink boxes give us the complete set of T-Coil parameters as a Function of R1, C1, and δ
Presenter
Presentation Notes
Continuing on with the derivation of the T-Coil circuit elements, we remember that we have previously defined Kx in terms of the coefficient of coupling k as shown. We also know that k, the coefficient of coupling as a function of Delta, the damping factor. Therefore we can now solve for Kx as a function of Delta. We know from the original set of equation describing the T-Coil that Lt must equal R1^2 times C1. We know that Ls = Lr = (1+Kx)(Lt/4) and we know Kx. Therefore we now know Ls and Lr as a function of Delta Finally, the original set of equations set the bridging capacitance Cb, as equal to KxC1/4. Since we know Kx as a function of Delta, we can write Cb as a function of Delta and C1. It is C1/(16 Delta^2) The bottom line is that the T-coil parameters are all set by Delta, R1 and C1. Once we choose a desired Delta, we can calculate the required values for k, Ls, Lr, and Cb
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Solving for bandwidth in this way gives:
For the MFED case (δ=Sqrt(3)/2), f3dB is:
BandwidthImprovementFactor
One can find the bandwidth of any second order system using this equation
We can solve for the bandwidth of the normal equation by substituting j2πf for s, • Then finding the magnitude by taking the square root of the sum of the real part squared
and the imaginary part squared• And then solving this equation for the point it is 0.707 as a function of f (frequency)
Presenter
Presentation Notes
What is the bandwidth of a second order system and in particular of a T-Coil filter? I solve this in the general case for the standard form equation as the result provides a useful tool for calculating the bandwidth of any second order filter, T-coil or not! To actually solve for the bandwidth, I used Mathematica—another program I highly recommend as it is capable of solving symbolic algebra equations. In particular, I begin by substituting into the equation F(s) s = jw. I then solve for the magnitude of the this equation by taking the Sqrt of the sum of the squares of the real part and the imaginary part of F(jw) equation. At w=0, the equation will be 1. At some frequency, the function will be Sqrt(2)/2. It is this frequency that represents the 3 dB down point and therefore the bandwidth of the filter. The end result is the first equation for f3db. I now multiply top and bottom of this equation by 2 Delta to obtain the second equation for f3db. We can now determine the bandwidth of any second order system that is represented in standard form by simple substitution of the term in front of “s” for 2 Delta T in the bandwidth equation!!! For the case of the T-coil, we see that 2 Delta T is equal to R1C1/2. This gives the bandwidth for the T-coil described by the equation f3db_T-Coil. It is now purely a function of Delta, R1 and C1. If we let Delta = Sqrt(3)/2, we obtain the equation for T-coil bandwidth of 2.72/(2 pi R1 C1) thus proving the assertion that the T-coil provides a bandwidth improvement factor of 2.72 while keeping the step response MFED.
• Maximally Flat Envelope Delay (MFED) is the kind of filter required if the desire is to have good step response in the time domain. By good, it is meant that there will be little to no overshoot when a unit step function is applied at the input, while achieving maximum possible bandwidth under that constraint.
• We will very shortly show that this requires a value of δ = Sqrt(3)/2 = 0.8666 for a second order Low Pass Filter
• It is acceptable in almost all circumstances to trade delay time for more bandwidth.
• However, we must delay all frequencies the exact same amount to prevent overshoot and ring in a time domain step response.
• The time domain expression for an ideal time delay is given by the DiracDelta function:
Presenter
Presentation Notes
At this point we need a slight detour into some theory. We need to look at the ideal time delay function. Trading off delay time for more bandwidth is considered a good and acceptable. However, we need to delay all frequencies the exact same amount if we are to keep waveform integrity—i.e. no overshoot or ring. The function that does this is called the DiracDelta function
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Transforming the time domain function into the frequency domain gives:
• Not a rational function so it cannot be realized with standard RLC components
Transforming the DiracDelta function into the frequency domain gives the function shown in the slide. This function is not rational so it cannot be realized with standard RLC components, but it can be approximated. The approximation used is called a Maximally Flat Envelope Delay or MFED filter.
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Phase & Phase Delay of the Ideal Time Delay Function
This slide looks at the phase and envelope delay of the ideal time delay function. I obtained this by once again using Mathematica. To begin, I substituted for s in the ideal time delay function jw. I converted the result to a trig function using the ExpToTrig function of Mathematica. This gives the result of cos – j sin. Clearly the magnitude of this function is unity. The phase is the arctan of the imaginary part divided by the real part. This becomes simply – to w. Phase delay is defined as the phase divided by the radian frequency w. In this case the result is –to. Envelope delay is defined as the derivative of the phase with respect to radian frequency. In this case, the result is the same as the phase delay namely –to While we can’t actually implement this circuit, it is useful to see what the ideal result would be. We will shortly how we actually implement a reasonable approximation to the problem. The result will be what we call a maximally flat envelope delay function
Solve for phase, phase delay, and envelope delay of the normalized two pole filter gives
Substitutes=jω
Find real partAnd Imaginary part
Definition of PhaseDefinition of Phase Delay
Presenter
Presentation Notes
Phase is closely related to time delay. We can use a program like Mathmatica (a program I highly recommend) to solve the standard functions for the phase. Mathematica can then be used to solve for the phase delay witch is defined as the negative value of the phase divided by the radian frequency. Observe that the result has units of time. Envelope delay is defined as minus the derivative of the phase with respect to radian frequency. Again the result has units of time. Envelope delay is a more sensitive measure for defining the filter parameters we wish to create than pure phase delay. An MFED filter is then created by choosing parameters that keeps the envelop delay as close to a constant as possible for to the highest possible frequency. If envelop delay peaks in the higher frequencies, then there will be overshoot.
This graph show a Mathematica plot of phase delay for a simple RC circuit depicted in the time domain Phase delay is the time corresponding to the phase lag, i.e. a phase lag of 45 degrees at 100 MHz corresponds to 1/8 of the period of 10 ns or 1.25 ns.
Phase Delay• Phase delay ties frequency response to the step response. • It is the time corresponding to the phase lag, i.e. a phase lag of 45 degrees at
100 MHz corresponds to 1/8 of the period of 10 ns or 1.25 ns. • Phase delay gives some idea as to what happens to the high-frequency
components of a step response. • If the phase delay peaks (exceeds the low-frequency value) you can expect to
see high-frequency components late in the step response. This causes ringing. Envelope Delay
• Envelope delay (also known as group delay) is not as intuitive, but it is easier to understand mathematically.
• It is a more sensitive measure of aberrations than phase delay. • If envelope delay is flat with increasing frequency, then the phase delay will be
also. • It is the envelope delay that is used as the prime measure to approximate a
constant delay.
Presenter
Presentation Notes
Envelope delay is the derivative of the phase delay with respect to the radian frequency ω. It also has units of time. At low frequencies, for the circuits we are studying in this seminar, the low frequency phase delay is equal to the low frequency envelope delay. Low frequency means the delay as ω approaches zero.
Observe that there is no peaking in the response as ω becomes large• Low Frequency delay is 2 δ T = 1.732
Presenter
Presentation Notes
As an example, consider a plot of envelope and phase delay vs w for the case of delta = .866. Observe that the plot is flat right out to the point it begins to roll off. It has delayed all frequencies equally until it can do no more. This filter would have a good step response.
Now there is peaking in the response as ω becomes large• Causes Ring in the time domain Step Response• Low Frequency delay is 2 δ T = 1.0
Presenter
Presentation Notes
The phase and envelope delay of this filter with a delta of .5 peaks as w increases. In this case, the high frequency delay is approximately twice that of the low frequency delay. Thus the high frequency components of the waveform are delay’ed with respect to the low frequency elements. This will cause ring in a step response.
A class of transfer functions called Maximally Flat Envelope Delay (MFED) has been determined:
When low-pass filters are implemented to match the MFED response, they will provide maximum bandwidth with minimum overshoot and ringThey are an attempt to make the envelope delay completely flat, with no variation with respect to frequency, so that an input step response will be delayed in time but not distorted in shapeFilters implemented to these criteria are not perfect, but they are the best that can be achievedThe derivation of these filters is quite complex, involving Bessel polynomials, but the results are easily usedThe step response of these functions is good, with overshoot of less than 0.76%
Presenter
Presentation Notes
So far, we have stated the fact that an MFED function provides the best step response. But we haven’t derived how to determine the parameters that make up an MFED filter.
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Suppose a low-pass filter exists as defined in the equations below• Then the resulting filter will be MFED• Low Frequency Phase Delay is the phase delay when ω=0
This function can be found in almost any filter textbook. Observe that the low frequency phase delay is a1/a0. If one assumes the normalized form for a low pass filter; i.e. F(s) = 1/(T2s2+2δTs+1), then the low frequency delay would be 2δT. For MFED fliters, δ = Sqrt(3)/2 (We will prove this assertion in a couple of slides). Thus the low frequency delay for an MFED two pole filter is T Sqrt(3).
•Using the previous table, a second order MFED filter is F(s) shown below
•Comparing this against the standard form for a two pole filter and solving for δ gives
Presenter
Presentation Notes
The result for a two pole filter. If we compare the ideal MFED 2 pole filter against the standard form two pole filter, we can immediately show that 2 Delta T must equal 1 and T^2 must equal 1/3. Combining and solving gives the relationship that Delta = SQRT(3)/2 It is here that we prove that δ must equal Sqrt(3)/2 for the filter to be MFED
Here is a table containing required element values for the T-coils for different values of damping factors. Again the derivation of these is beyond the scope of this presentation.
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Let R1 = 50 Ω and C1 = 1 pF, then
• Bandwidth should equal 8.66 GHz (2.72 times the bandwidth for just the RC—3.18 GHz)
• Input impedance should equal 50 Ω• Step response should be MFED
An example T-Coil filter using Genesys. The values for R1 and C1 are 50 Ohms and 1 pF respectively. These values for R and C would give a bandwidth of 3183 MHz. But with T-coil peaking we should obtain a value of 8.66 GHz for the bandwidth. This is a remarkable result. It is important to remember that this is a purely passive network made up of inductors and capacitors. Inductors and capacitors do not produce noise! Because it is virtually always possible to trade bandwidth for gain, this is like having a noise free amplifier. Yes these circuits are a little more difficult to construct because of the inductance (mutual and otherwise) especially on an IC. But the benefits outweigh the difficulties. Inductance is one of three primary passive elements available to the analog engineer. Does it make sense to throw away 1/3 of your tools because it is “difficult to implement”? I guarantee that for the engineer who figures out how to use these elements will be the winner and those that don’t will be the people who will lose for themselves and their companies.
Here is the Genesys schematic for the example problem. The component values are calculated using the previously defined equations. These equations have been placed inside of the equation editor of Genesys to automatically calculate the values and insert them directly into the components.
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The tune button allows a variable to be changed dynamically while you watch.
Once again, here is the Genesys input screen for the T-coil. Observe in the upper right hand corner, there are a couple of variables shown. These variables have been set as “tuneable”. The value is easily set by simply clicking on the frame containing the value and using the mouse wheel to increase or decrease the component value. As this is done, the output files all automatically update their values so that the effect of the change can be seen immediately. This tune capability is extremely helpful when trying to arrive at precise component values. Also observe that other components are calculated in the equation editor. Data is input from other component values and the appropriate equations are used to calculate the remaining component values. Again this can be very helpful when “gang” tuning is desired.
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Equations to calculate the component values automatically
Resultant values calculated by the equations
Setup Design Formulas Using the EquationEditor in Agilent Genesys
Here is the equation editor inside of Genesys showing the equations used to calculate the various component values. We only need to enter the value for CL, RL and Del and the component values are calculated automatically. The ? Before the value “1” in the first equation for CL means that this value will be placed in the “tune” button section of Genesys. This allows us to change this value very easily and see instantly what happens to the rest of the parameters.
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Genesys Frequency Response for T-CoilPeaked CircuitObserve: Genesys simulated bandwidth is 8.66 GHz vs. theoretical value of 8.66 GHz
Here is the Genesys simulated frequency response for the T-Coil example. Observe how the theoretical predicted value is identical to the simulated value
A Genesys simulation of the T-Coil Circuit showing the step response. The input is an ideal step of 20 ma. This produces a voltage of 0.5 volts at the output of the filter (capacitor C1). It is half a volt because the impedance being seen is 25 Ohms—50 Ohms from the filter and 50 Ohms as the Port 1 output impedance. The step response is perfect with no overshoot.
Observe that the input impedance Zin is a constant 50 Ohms (equal to the termination resistance) for all frequencies. This is true as long as the component elements remain ideal. Of course, once the component elements start to deviate from ideal, all bets are off. S11 is the reflection coefficient at the input to the network. Observe that this parameter, at below -100 dB, is about as ideal as it comes.
Genesys simulation for VSWR for the T-Coil example. The ideal value for this parameter is 1. Once again, this shows that this would make an excellent termination for a transmission line.
Here is the group delay for the T-Coil. This represents an ideal group delay for an MFED filter. This is in very close agreement to the theoretical. Observe that the low frequency value is 25 psec. We know from previous work that the low frequency delay is a1/a0 which for a T-Coil is equal to R1C1/2. This equals (50Ω)(1pF)/2 which is 25ps thus bering out the theory.
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What about other values for δ
So far, we have looked at the special case of an MFED filter response
It is useful to consider other values of δ that will produce different kinds of two pole filters
Compare the following kinds of filters:
• Straight RC filter—no peaking
• MFED δ = SQRT(3)/2
• MFA (Maximally Flat Amplitude) otherwise known as a Butterworth
For completeness, it is useful to look at other values of Delta and compare the results against each other. In this way we can see how the response changes as delta changes. I will use four values for delta. 1) a straight RC; delta is infinity, 2) MFED 3) Butterworth Delta = SQRT(2)/2 and 4) Delta = 0.5
Here is the Genesys schematic for the four circuits. Each has the appropriate component values to create the desired response. Observe that the case where Delta = 0.5, k is zero. This represents a limiting case
Here is the frequency response for the four circuits. The plot in green shows the straight RC case, and of course it has the lowest bandwidth by a large margin. The bandwidth is only 3180 MHz. The red plot shows the frequency response for the MFED case. Its bandwidth is 8659 MHz—exactly as predicted. The orange plot show the bandwidth for the Butterworth filter (Delta = 0.707). This is sometimes know as a Maximally Flat Amplitude Response as it gives the most bandwidth without overshooting on a frequency amplitude plot such as this plot. In fact, observe how the curve does indeed provide as much bandwidth as possible without ever exceeding 0dB. The actual bandwidth for this case is 9005 MHz—again right on theory. Finally, the blue trace shows the frequency response when delta = 0.5. In this case the amplitude peaks at about 1.25 dB exceeding the low frequency value. However the bandwidth is 8090 MHz. This is less bandwidth than both the Butterworth and the MFED case.
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Take the Derivative of f3dB_T-Coil with respect to δ, set it equal to 0 and solve for δ gives a maximum at δ=1/SQRT(2)
This slide shows a plot of bandwidth for the T-Coil Circuit vs Delta. Observe that the maximum bandwidth occurs at Delta = 1/SQRT(2). This is the Butterworth filter. As delta is decreased from the 0.707 vlaue, the bandwidth decreases. Thus the Butterworth filter represents the maximum bandwidth possible out of a two pole filter.
Here we have the time domain step response for the four examples. Again the purple line represents the straight RC filter. As expected, it has the slowest risetime of all the filters. That’s why we invented the peaking netwo0rks in the first place! The blue line is the MFED filter. Observe that the risetime is much less than the RC filter. Also observe that there is no overshoot. The orange trace is the Butterworth filter. It is approximately the same as the MFED filter in terms of speed, but it overshoots. Finally, the purple line is the case of Delta = 0.5. This case has significant overshoot. Risetime is defined as the time required to go from 10% to 90% of final value
This plot shows the input impedance for each of the three T-Coil cases. For all three of these cases, the impedance is exactly 50 Ohms. Impressive! I did not show the RC case as it will clearly not be 50 Ohms.
Here is the output impedance for the three T-Coil cases (taken at the load capacitor). Observe that the output impedance looks pretty close to 25 Ohms up to some pretty high frequencies. The low frequency value is 25 ohms because looking back into this port, the system see two 50 Ohm resistors in parallel; 50 ohms from the source and 50 Ohms from the terminating impedance. For the MFED case, the output impedance just rolls off with frequency. But both of the other two cases have the output impedance peak at near the bandwidth frequencies.
Shown is the group or envelope delay for the four circuits. The RC case shown in orange, simply rolls off early. Observe that its low frequency value is twice that of the T-coil cases. This follows from the theory. In this case, the low frequency value, equal to a1/a0 is simply equal to R1C1. That value is 50 ns for the example. The red trace is the MFED case. This shows that there is no increase in delay at high frequencies. Thus all of the frequencies arrive at the same relative time and overshoot is avoided. Both of the other cases show the delay increasing over the low frequency value at high frequencies. Thus it takes longer for the hifh frequency components to reach the output of the circuit. This causes ring in the time domain.
Monte Carlo Transient Response with ±5% part Variation
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Monte Carlo Frequency Response with ±5% Part Variation
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Monte Carlo Analysis for Group Delay with ±5% Component VariationFrom this graph, we see that the parameter variation mainly affects the low frequency delay
– At high frequencies, there is little peaking above the low frequency delay
– This is why the step response continues to look good while there is significant variation in bandwidth
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Monte Carlo Analysis for Input Impedance with ±5% Component Variation
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Monte Carlo Analysis for VSWR with ±5% Component Variation
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Monte Carlo Analysis for S11 with ±5% Component Variation
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Physical Design of T-Coils Components: Spiral Inductors•All inductors have some stray capacitance between windings.
•This capacitance shows up in parallel with the bridging capacitance Cb
•If you know the self resonant frequency of the inductors, you can estimate the stray capacitance using the formula below
•Once you know the capacitance, subtract it from Cb
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Momentum GX: 3D-Planar Electromagnetic Simulation for Genesys
Sub
Eddy Currents
Displacement Currents
Use Momentum GX to accurately model:
Self & mutual inductance
Self-resonance frequency
Displacement currents from spiral to substrate thru oxide capacitance
Eddy Currents in substrate due time varying magnetic fields Spiral to Substrate Insulation
Here is one physical implementation of a T-coil using bond wires to an IC. Two pads are used with a bond wire going to each pad to the location on the IC where the load capacitance is located. The Bond wires create the two legs of the T-coil; Ls and Lr The T-Coil is then driven from the pad attached to Ls and the termination load resistance is attached to the other pad. The individual inductors are arranged in such a way as to create mutual inductance between the two wires. Finally stray capacitance is used as the bridging capacitance between the two pads. This might seem a little complex and difficult to implement, but in reality it is pretty easy. The technique was used by companies like Tektronix going as far back as the early 70’s. These days, it is actually easier to implement these devices inside of a chip because the needed values are so small. As device ft’s have increased, the load capacitors have decreased. Instead of needing nH to implement the required inductors, pH are now what is needed. It almost requires an IC to implement inductors this small. Great strides have been made in device physics to get ever higher ft’s. Even so, still higher speed performance is asked for by the market place. This ends up requiring techniques developed in the past to squeeze the last bit of performance out of circuits when the device speeds simply weren’t there; techniques such as T-coils, that for a time were un-necessary because of the increased device speed, now comes back as necessary. Today's engineer must re-invent the techniques of the past. This cycle has repeated several times.
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Additional Resources
For a copy of this presentation and to download the T-Coils Genesys design workspace template, go to: www.allenhollister.com or email [email protected]
Interested in learning more about wideband amplifier design, see Allen’s course on “Wideband/HF Amplifier Design Techniques” offered through Besser Associates
You can order your copy of “Wideband Amplifier Design” from Amazon or SciTech Publishing
To download your Free evaluation copy of Agilent Genesys and Momentum GX software, please follow this link: http://eesof.tm.agilent.com/products/genesys/
