I would like to model a piece of cable (less than 5m) over a frequency range of DC to 1 MHz. I am however doubting if I can approximate it by a lumped parameter model (mainly at 1 MHz) or if I need to model it as a continuous transmission line. If I am correct, lumped parameters can be used as long as the physical dimensions of the system (here: cable length) are sufficiently below the wavelength lambda. Since lambda (in free space) can be calculated using the speed of light c and f, for 1 MHz I get: lambda = 300000000/1000000 = 300 m (approximately). Since my physical system is much smaller, I suppose a lumped parameter representation is sufficiently accurate. However, in transmission line theory, the wavelength is derived through the propagation constant gamma = alpha + jbeta. Gamma is calculated through the cable's impedance and admittance and the corresponding wavelength can be calculated as lambda = 2pi/beta. That would thus mean that the physical properties (R,L,C) of my cable will determine the wavelength. Does that also mean that two different cables of the same length would possibly need to be modeled as a continuous or a lumped parameter model, just because we would choose thicker wires or have more spacing between the wires? I am a bit confused on the approach that should be followed and I am happy to receive your input.

I would like to model a piece of cable (less than 5m) over a frequency range of DC to \$1\mathrm{MHz}\$. I am however doubting if I can approximate it by a lumped parameter model (mainly at \$1\mathrm{MHz}\$) or if I need to model it as a continuous transmission line. If I am correct, lumped parameters can be used as long as the physical dimensions of the system (here: cable length) are sufficiently below the wavelength lambda. Since lambda (in free space) can be calculated using the speed of light \$c\$ and \$f\$, for \$1\mathrm{MHz}\$ I get: $$\lambda = \frac{300000000\text{ km/s}}{1000000\text{ Hz}} = 300\mathrm{ m}\text{ (approximately)}. $$ Since my physical system is much smaller, I suppose a lumped parameter representation is sufficiently accurate. However, in transmission line theory, the wavelength is derived through the propagation constant $$ \gamma = \alpha + j\cdot\beta. $$ \$\gamma\$ is calculated through the cable's impedance and admittance and the corresponding wavelength can be calculated as $$ \lambda = 2\cdot\frac{\pi}{\beta}. $$ That would thus mean that the physical properties (\$R,L,C\$) of my cable will determine the wavelength. Does that also mean that two different cables of the same length would possibly need to be modeled as a continuous or a lumped parameter model, just because we would choose thicker wires or have more spacing between the wires? I am a bit confused on the approach that should be followed and I am happy to receive your input.