Parasitic effects on passive elements at high frequency

Question

What would the magnitude response curve for a resistor, inductor and capacitor look like with parasitic effects not ideal components? From what I have gathered they would look something along the lines of:

These are log-log graphs.

Resistor:

Inductor:

Capacitor:

Resistor: At high frequency the inductor characteristic dominates jwl hence impedance increase, capacitance would go to zero and R would become negligible.

Inductor: there is the peak there due to the resonance otherwise straight line gradient 1.

Capacitor: straight line gradient -1, not sure of any parasitic effects here?

Are these correct? If not I would love to hear your contributions. If my explanations are lacking anything please add on for better understanding.

To add on to this, if I were to draw the circuit symbols of these non-ideal passive components what would they look like?

Answer 1

I think the graphs you have are not correct in general. You can't draw generalizations without discussing the frequency range of interest and physical construction of the components.

Essentially every real component can be modeled as a combination of ideal components. The more ideal components you keep adding the higher order and more precise your model becomes. Once you do the transfer function of this "real approximation" model using ideal components you will get a bode plot which will show you how the part will behavior under various frequencies.

It is true that often a resistor will first start looking like an inductor, a capacitor first like an inductor and an inductor first like a capacitor as you get outside of their expected performance range, but this is very much a rule of thumb to be taken with a grain of salt.

For example below are some first order approximations that are good enough for most EE work and rooted in physics...but precise applications may require more ideal components to model various behavior than is even shown here.

Here is a resistor:

Here is a capacitor:

Here is an inductor:

Here is a decent intro to bode plots.

Addendum

Here is a Vishay study on frequency response of thin-film resistors

Answer 2

Here's some general points;

• tracks and axial parts are 1nH/mm +/-50% typ depending on geometry
• shunt capacitance depends on surface area/gap ratio
• crosstalk can be computed as coplanar stripline in nH/cm and pF/cm for some geometry
  • transfer function depending on input/path impedance ratio.
• Common Mode coupling depends on stray EMF and MMF , imbalanced impedances, proximity
• CM noise is common and is reduced with balanced low impedances, CM choke (= "Baluns") to raise and balance the CM Z
  • then add shunt ground caps as Pi filters to attenuate with 2nd order CM noise reduction.

Answer 3

In general, refer to the component datasheets or characteristics, when available.

There are too many types to go through in detail, but this is an illustration of what to expect from chip resistors:

From Frequency Response of Thin Film Chip Resistors - Vishay:

Generally speaking, the larger the component, the lower the cutoff/break frequencies will be. This shows 0201 outperforming 0402/0603, and it seems there's some competition between the latter, but 0402 generally comes out on top.

For resistors of small values (under 100 ohms or so), inductance dominates first, and the curve bends upward. Larger, capacitance dominates first, and the curve bends down.

The curve diverges sooner, the farther the value is from that point -- that is, a 10Ω or 1k diverge 10 times lower than 100, etc.

The "flattest" resistance (the value for which flat/resistive bandwidth is maximum) varies with construction type. We can expect spiral-cut and wirewound types to have a higher "best" impedance.

Fundamentally, what this impedance is, is the characteristic impedance of the assembly. That is, there are leads with some stray inductance, end caps or pads with some capacitance, and a distribution of both along the resistive element itself. The characteristic impedance is given by \$Z_0 = \frac{L}{C}\$.