Some Notes on CaMF Program

2000-01-20 by Jouni Verronen

CaMF is basically for calculating a three element pi or T circuit, which can be regarded as a filter or a matching block.

In practical radio circuits lowpass filters are common, because nonlinearities in active components produce harmonic frequencies, which tend to be harmful. For impedance matching a highpass circuit is frequently chosen and elegant for the reason that a DC block capacitor, which may be needed, is a part of the matching circuit. With impedance transformation often some filtering properties are desirable.

All LP or HP filter design procedures do not necessary match well with practical needs. Classic LP designs are flat from DC, when very often just a reasonably broad passband and good harmonics attenuation are the main requirements. Also one generally has to figure out at which frequency fc the response is allowed to be down a certain amount.

In this program you give the center frequency of the RF band and then you can look around how far the match is satisfactory and how attenuation increases while changing the circuit Q.

For many narrow band cases this basic 3 element circuit is all that is needed. The program has also some use in more demanding cases - with broad bands, high impedance transform ratios, high attenuations. With it one can calculate starting values for cascaded blocks, and then put the circuit into a network analysis program for evaluating and optimizing.

```        CaMF can be used directly for the following calculations:

1) a three element LP (or HP) filter to be inserted in e.g. 50 ohm
line (source and load impedances the same, third order filter with
three elements).

2) a L-section for impedance transform  (minimum Q)

3) a pi-filter or T-filter with impedance transformation
(higher Q, source and load impedances differ)
```
These are often thought as different cases, but actually are closely related. The first two can be regarded as special cases of the third. CaMF calculates a basic three element LP pi-circuit and the corresponding tree element HP T-circuit, which both make the desired impedance match at the design frequency. ### How to use it

Input values can be given by hitting a key:

```           key:

f         fo,     operating frequency
x         fx,     a freq. of interest for attenuation and match
1         R1,     termination, high side
2         R2,     termination, low side
q         Q1,     loaded Q for the high impedance end
m                 calculates with minimum Q  (L-section)
```
Terminations are resistive. They can be equal or R1 > R2. Giving 0 (bare enter) for fx sets fx=fo.

When using the program the main principle is to vary the circuit Q to find out the best combination of bandwidth and out of band attenuation with the component values available. Q can be tuned by PgUp/PgDn keys. Ins/Del changes the increment. Q tunes down to the minimum value at which the match is still possible. Tuning towards high Q values the circuit begins to be more like bandpass with more or less unrealistic component values.

Attenuation and also return loss are calculated for one variable frequency fx, which can also be tuned by the arrow keys. Up/Down changes the increment. So it is easy to look around the design frequency fo, how match and attenuation change while tuning the circuit Q.

### Comparing with Butterworth and Tchebyscheff

If we give fo = 65 MHz and Q1 = 1.0, we get very close to a Tchebyscheff design for 0.15 dB ripple and -0.15 dB cutoff at about 74 MHz for the lowpass circuit (-3 dB abt 100 MHz).

In the Butterworth design the series coil has higher inductance and the capacitors are smaller, and the best return loss is at zero frequency.

If the impedance step is large, as in matching an input of a bipolar RF transistor power stage, the necessary Q for a one L-section matching circuit becomes high, which leads to narrow passband, abrupt tuning and higher losses.

The passband becomes wider, if the transformation is done in two or more steps. Most often the same Q is used for the sections. In the case of two sections an intermediate impedance level at the joint of the sections is

Rm = sqrt(R1*R2) A HP-LP set is common between transistor stages, because the collector choke and DC blocking capacitor can be embedded in the matching circuit. In HP-LP or LP-HP case the passband broadens and flattens quite symmetrically around the design frequency fo. At first not so obvious is to find that in the case HP-HP the passband broadens for the most part downwards of fo, in the case LP-LP upwards.

### Adding components for wider passband

One basic tip:

Add preferably a serial LC on the high impedance side and a parallel LC on the low impedance side. The added LC circuits are resonant at fo. These tend to make the passband more flat by compensating reactances around the center frequency. ### Cascading pi-sections for higher harmonic attenuation

Say you have calculated one LP pi-filter section to be inserted into a 50 ohm line. Given circuit Q is around 1. The passband is OK, but the harmonic attenuation is not high enough. Question: is it all right to add another similar section after it?

Yes, generally it can be done, and match at the design frequency fo is good. And every section adds up to the total harmonic attenuation roughly the amount it has alone. However the sections do interact as soon as the frequency differs from fo, and a slight tuning of one or two capacitor improves the match by side of fo. For cascading two pi-sections to form a 5'th order lowpass a slight, say 5 % decrease in the center capacitor value makes the passband broader and flatter without much affecting harmonics attenuation.

Higher order filters are more complex to tune and for designing them there are better programs than this.

One simple way to get some more harmonic attenuation is to replace the coil with a series LC circuit having the same reactance at the design frequency with the original coil. In this case the passband will narrow. This suits best for tuned circuits.

### Adding resonances for higher harmonic attenuation

We are considering the basic two shunt capacitor series inductance lowpass filter block.

Series inductance can be added to shunt capacitors to make them resonant at harmonic frequencies. Likewise the series inductance can be replaced by a parallel circuit resonant at some higher frequency. At the design frequency these circuits must represent the same reactance as the original component. I have shown an example in CaLC3.txt.

These additions to the basic lowpass circuit do not have much effect on the design frequency and downwards. It must be noted, that attenuation at higher harmonics above the notch frequencies will inevitably suffer. A section with no traps may be needed. A linear circuit analyzer program is the right tool to proceed with.

Capacitors to ground can be replaced by open stubs very simply. Reactances must be the same at the design frequency. Check my Xline program. One thing to remember, however, is that depending on the length of the open line it can turn inductive or high impedance at higher harmonic frequencies.

A corresponding microstrip transmission line for the shunt coil in the HP circuit can be calculated using Xline program. But if the transmission line equivalent for the series coil in the LP circuit is calculated using Xline, the result is not exactly right. There is some difference if the both ends are off ground comparing to the case when the other end is grounded. In the latter case it is possible to determine a single reactance as an equivalent for a lossless transmission line. In the former case a pi or T circuit is necessary.

Using Tline program a one section impedance transformer can be resolved iteratively. The length of the line is tuned up until the parallel resistance seen at the end is right.

In my opinion microstrips or striplines are most useful as inductive elements at VHF and low UHF. For capacitive components ceramic capacitors, especially HQ types, have low losses and do not need much pc-board area. At higher microwave frequencies capacitive stubs become necessary as lumped capacitors become impractical.

### On simplifications

This is intended to be a basic easy to use tool for LC impedance match. The following simplifications were chosen.

- terminations are resistive

- components are ideal, with no losses or paracitics

If high Q is used, it is wise to check loss at fo with a circuit analysis program using lossy components.