# RF Filter Design Tool

## Overview

The RF Filter Design Tool is a comprehensive synthesis framework for generating RF and microwave filters from normalized lowpass prototypes. It supports multiple filter topologies, response types, and implementation technologies.

## Filter Response Types

All filter implementations begin with normalized lowpass prototype coefficients, which are then transformed based on the desired filter topology.

### Butterworth

Maximally flat magnitude response in the passband. No ripple.

**Formula:**
```
gₖ = 2 × sin(π(2k-1)/(2N))    for k = 1 to N
```

**Use case:** General-purpose filters where phase linearity is not critical.

### Chebyshev

Equal-ripple response in the passband, steeper rolloff than Butterworth.

**Parameters:**
- Ripple: 0.01 – 2.0 dB (passband)

**Formula:**
```
β = ln(1 / tanh(Ripple / 17.37))
γ = sinh(β / (2N))
g₁ = 2a₁ / γ
gₖ = (4aₖ₋₁aₖ) / (bₖ₋₁gₖ₋₁)   for k = 2 to N

where:
  aₖ = sin(π(2k-1)/(2N))
  bₖ = γ² + sin²(kπ/N)
```

**Use case:** Applications requiring sharp selectivity with moderate ripple tolerance.

### Bessel

Maximally flat group delay (linear phase). Pre-calculated coefficients from Zverev tables.

**Use case:** Pulse shaping, data transmission, any application requiring minimal phase distortion.

### Gaussian

Gaussian-shaped impulse response. Pre-calculated coefficients from Zverev tables.

**Use case:** Time-domain applications, pulse filters.

### Legendre

Steepest monotonic rolloff. Pre-calculated coefficients from Zverev tables.

**Use case:** Applications requiring sharp selectivity without passband ripple.

## Filter Implementations

The tool supports the following synthesis topologies:

| Implementation | Filter Types | Description |
|----------------|--------------|-------------|
| [LC Ladder](/RFCircuitSynthesis/Filters/LC_Canonical/index) | LP, HP, BP, BS | Canonical LC network (CLC or LCL) |
| **LC Direct Coupled** | BP | Resonators with direct coupling |
| [Stepped Impedance](/RFCircuitSynthesis/Filters/SteppedZ/index) | LP | Alternating high/low impedance TL sections |
| [Quarter-Wavelength](/RFCircuitSynthesis/Filters/QuarterWave/index) | BP, BS | λ/4 TL with open/short stubs |
| [Capacitively-Coupled Shunt Resonators](/RFCircuitSynthesis/Filters/CapCoupledShuntResonators/index) | BP | λ/4 stubs with series capacitors |
| [Side-Coupled](/RFCircuitSynthesis/Filters/SideCoupled/index) | BP | Coupled parallel resonators |
| [End-Coupled](/RFCircuitSynthesis/Filters/EndCoupled/index) | BP | End-gap coupled resonators |
| **Semilumped** | LP, HP | Hybrid LC + TL implementation |

See individual filter documentation for detailed synthesis equations.


## Design Flow

1. **Select response type** (Butterworth, Chebyshev, etc.)
2. **Choose filter class** (Lowpass, Highpass, Bandpass, Bandstop)
3. **Set specifications** (fc, BW, order, ripple if applicable)
4. **Select implementation** (LC Ladder, Stepped Impedance, etc.)
5. **Choose TL technology** (Ideal or Microstrip)
6. **Generate schematic** → Tool outputs netlist with component values


## References

[1] Zverev, A. I. (1967). *Handbook of Filter Synthesis*. Wiley.

[2] Matthaei, G. L., Young, L., & Jones, E. M. T. (1964). *Microwave Filters, Impedance-Matching Networks, and Coupling Structures*. Artech House.

[3] Pozar, D. M. (2012). *Microwave Engineering* (4th ed.). Wiley.

[4] Hong, J.-S., & Lancaster, M. J. (2001). *Microstrip Filters for RF/Microwave Applications*. Wiley.

```{toctree}
:maxdepth: 1
/RFCircuitSynthesis/index
```