Circuit bench

Put inductors, capacitors, resistors, coax and transformers in a line between a source and a load, and see what reaches the load across a sweep, what the source sees, and how much voltage and current each part carries.

Build the circuit

Source, load and frequency

Source resistance

Load resistance

Operating frequency

MHz

Where the part stresses are reported.

Power available

Into a matched load.

Sweep from

MHz

Sweep to

MHz

Parts, from the source to the load

1 Capacitor to ground
Capacitance
2 Series inductor
Inductance
3 Capacitor to ground
Capacitance
4 Series inductor
Inductance
5 Capacitor to ground
Capacitance

Add a part at the load end

Ideal parts between the source and its internal resistance on the left and the load on the right; the bottom line is the common return. Numbers match the parts list.

Loss at 7.15 MHz: 0.0996 dB
The source sees: 48.73 Ω − j14.98 Ω
SWR at the source: 1.35 : 1
Power to the load: 97.7 W of 100 W

At 7.15 MHz the load receives 97.7 W of the 100 W the source can deliver, a loss of 0.0996 dB. Return loss at the source is 16.4 dB.

Response across the sweep

0 dB means all the power the source can deliver reaches the load. f marks the operating frequency and 2f to 5f its harmonics.

Measured against the 50 Ω source resistance.

The trace runs from the bottom of the sweep to the top; the dot is the operating frequency. The center is a perfect match.

What each part carries

At 7.15 MHz with 100 W available. Values are RMS; for a sine wave the peak is √2 times the RMS value. For a line or coax, Peak is the highest voltage anywhere along it: on a mismatched line the forward and reflected waves add inside the line, so it can be higher than at either end. Values under a billionth of the largest in the circuit are shown as 0, since with ideal parts they are rounding error.

Part	Voltage RMS	Peak	Current RMS
1. capacitor to ground, 417 pF	72.2 V	102 V	1.35 A
2. series inductor, 1.25 µH	92.1 V	130 V	1.65 A
3. capacitor to ground, 718 pF	78.3 V	111 V	2.52 A
4. series inductor, 1.25 µH	107 V	152 V	1.92 A
5. capacitor to ground, 417 pF	69.9 V	98.9 V	1.31 A

Try this

Loss at 7.15 MHz is 0.0996 dB. The second harmonic at 14.3 MHz is down 24.2 dB and the third at 21.45 MHz 44.7 dB. Drag across the response chart to read any frequency.
At 14.2 MHz the network presents exactly 50 Ω. Tune away and it drifts: SWR 1.27 : 1 at 13 MHz and 1.33 : 1 at 15.5 MHz, so an L network matches one frequency at a time.
At 7.1 MHz the ideal inductor and capacitor resonate, the trap's impedance has no limit, and no signal reaches the load (the bench shows more than 150 dB). A real trap is finite: with a Q of 100, this 4.7 µH coil (209.7 Ω at 7.1 MHz) makes a trap of about 21 kΩ at resonance (E5A09, E5A04), a loss of 46.5 dB; with a Q of 200, 52.5 dB. On 14.2 MHz the trap is just a reactance in the line and the loss is 4.7 dB.
A 75 Ω line 3.48 m long, a quarter wave at 14.2 MHz on 0.66 cable, turns the 112.5 Ω load into 50 Ω. At 7.1 MHz it is an eighth wave and the SWR rises to 1.79 : 1.
With 100 W available, the inductor and the capacitor each carry 631 V RMS (892 V peak) at resonance, while the load sees 70.7 V. The voltages inside a resonant circuit rise with Q (E5A13).
The pad takes 6 dB at every frequency in the sweep, and the first resistor absorbs 3.32 W of the 10 W.

Apply it

Check a design before you build it: open a filter, matching network or attenuator from its tool with "Open in the circuit bench", change each part to a value you can buy, and watch the response, SWR and part voltages. Start from the low-pass filter designer, the matching network or the attenuator pads tool.
Choose capacitors and inductors from the stress table at your full power: a part rated below its peak voltage or current will fail. Inside a resonant circuit the voltages can be many times the voltage at the load (E5A13).
Real parts are not ideal. Every component combines its nominal reactance with parasitic reactance, which gives it a self-resonant frequency (E5D07); an inductor's self-resonance comes from the capacitance between its turns (E5D06), and above that frequency the inductor acts as a capacitor (G6A11). The bench uses ideal inductors and capacitors, so add a small series resistor to model a part's loss and keep designs well below the parts' self-resonance.
For diodes, transistors, oscillators and amplifiers use a full circuit simulator: ngspice, the open source SPICE simulator, handles diodes and bipolar, JFET and MOS transistors, and the Falstad circuit simulator animates the current as moving dots.

How it works

The bench solves the whole circuit by modified nodal analysis: one equation for each node voltage and for the current in each source, inductor, transformer and line, solved exactly at every frequency in the sweep.
A line is a two-port with A = D = cosh γl, B = Z0 sinh γl and C = sinh γl / Z0, the lossless form in Steer section 2.2.6 with the line loss added as attenuation. At zero frequency inductors and lines act as shorts and capacitors as open circuits.
Catalog coax uses the Belden datasheet loss and velocity factor with the characteristic impedance taken as real, as in the SWR tool; ideal lines have no loss.
An ideal transformer scales impedance by the square of its turns ratio: matching 600 ohms to 50 ohms takes a turns ratio of 3.46 to 1 (G5C07).
Values are RMS. Loss compares the power the source can deliver into a matched load with the power that reaches the load; SWR is measured against the source resistance.
Parts are ideal except resistors and catalog coax: no parasitic reactance, no self-resonance and no loss in inductors or capacitors (E5D07). An ideal trap at resonance therefore has no limit to its impedance. Where ideal parts cancel exactly, only rounding error is left, so the bench shows losses above 150 dB as more than 150 dB, impedances above 1 TΩ as an open circuit, and voltages and currents under a billionth of the largest in the circuit as 0.
For a line or coax, the peak voltage in the stress table is the highest anywhere along it, from the forward and reflected waves and the line loss. On a mismatched line they add inside the line (Ellingson section 3.13): a 50 Ω line three eighths of a wavelength long with a reflection coefficient of −0.6 at its load reaches 1.6 times the forward wave inside, against 1.17 and 0.4 times at its ends.
Its tests check it against the low-pass filter, matching network and attenuator tools and against the transmission line formulas, to at least five significant figures.

Learn more: Building your own gear

Sources: An Algorithm for Modified Nodal Analysis (Swarthmore College (E. Cheever)); Microwave and RF Design III, 2.2 Two-Port Networks (ABCD matrices) (NC State University (M. Steer)); Electromagnetics, Vol. 1, 3.15 Input Impedance of a Terminated Lossless Transmission Line (Virginia Tech (S. W. Ellingson)); Electromagnetics, Vol. 1, 3.13 Standing Waves (Virginia Tech (S. W. Ellingson)); Electromagnetics, Vol. 1, 3.8 Wave Propagation on a TEM Transmission Line (Virginia Tech (S. W. Ellingson)); 8240 (RG-58) technical data (Belden); 9258 (RG-8X) technical data (Belden); 8267 (RG-213) technical data (Belden); 8214 (RG-8, foam) technical data (Belden); 9913 (RG-8 type, semi-solid) technical data (Belden); 7810A (RF-400) technical data (Belden); Radio Mathematics (ARRL Handbook supplement) (ARRL); 2023-2027 General question pool (G5C07, G6A11) (NCVEC Question Pool Committee); 2024-2028 Extra question pool (E5A04, E5A09, E5A13, E5D06, E5D07) (NCVEC Question Pool Committee); Ngspice, the open source Spice circuit simulator (ngspice project); Circuit Simulator Applet (falstad.com)

Practice the exam questions: G5 Electrical Principles (General), G7 Practical Circuits (General), E5 Electrical Principles (Amateur Extra), E7 Practical Circuits (Amateur Extra)

Found something wrong or out of date? Report a problem with this tool on GitHub (a public issue; nothing is sent until you submit it there).