Marcel Merchat

RF and Microwave Engineer

```
pi
```

```
## [1] 3.141593
```

RF Small Signal AC Model | Amplifier Load Impedance (RL) |
---|---|

This parallel resonant circuit presents a matching impedance of 4-k\(\Omega\) at 20 MHz to the power amplifier. The 5-\(\Omega\) resistor is transformed to 4-k\(\Omega\) in this manner. |
The transformed load impedance R |

\[Q=\frac {f_o}{f_2-f_1}\]

\[B=\frac {f_o} {Q}\]

\[R_t=(1+Q^2) \cdot R_L\]

```
formatC(sqrt(Rt/RL-1), digits = 1, format = "f")
```

```
## [1] "28.3"
```

```
paste(formatC(fo/(Q1*1000), digits = 1, format = "f"), "-kHz", sep="")
```

```
## [1] "707.5-kHz"
```

```
## branch impedance X_c:
paste(formatC(Q * RL, digits = 1, format = "f"), "-Ohms", sep="")
```

```
## [1] "141.3-Ohms"
```

```
## branch capacitance C:
paste(formatC((1/ (w * Xc)) * 10^12, digits = 1, format = "f"), "-pF", sep="")
```

```
## [1] "56.3-pF"
```

```
## Branch inductance L:
paste(formatC(( Rt/(Q * w)) * 10^6 , digits = 3, format = "f"), "-uH", sep="")
```

```
## [1] "1.126-uH"
```

```
## [1] " * C:/Users/merch/OneDrive/Documents/LTSpice/RF/impedanceTransformers/imp_transfx/RF_impedance_Transformer_NoBW.asc"
## [2] "L_RFC c 0 1.12609942741738e-06 Ipk=12 Rser=0.0 Cpar=0"
## [3] "C1 c out 5.63049713708692e-11 V=2.5K Irms=0 Rser=0 Lser=0"
## [4] "RL out 0 5"
## [5] "Rt N01 c 4000"
## [6] "Vcc N01 0 SINE(018.921.1Meg) AC 1 Rser=0"
## [7] ";op"
## [8] ".ac lin 500 18.9Meg 21.1Meg"
## [9] ".backanno"
## [10] ".end"
## [11] "NA"
## [12] ""
## [13] ""
```

Impedance Response for simple Circuit with Default Bandwidth |
---|

The response of the transformer has a peak at 20-MHz where it matches the source resistance of 4-k\(\Omega\) for the power amplifier. The 707-kHz bandwidth is the only one possible for this simple circuit. |

Small Signal Model for 2-MHz Bandwidth at 100-MHz. |
---|

## Matching transformer |

```
paste("Qt =", formatC(Qt, digits = 1, format = "f"))
```

```
## [1] "Qt = 50.0"
```

```
paste("Qp =", formatC(sqrt((RL/Rt) * (Qt^2 + 1) - 1), digits = 2, format = "f"))
```

```
## [1] "Qp = 15.78"
```

```
paste("C2 = ", formatC((Qp/(w * RL)) * 10^12, digits = 1, format = "f"), "-pF", sep="")
```

```
## [1] "C2 = 25.1-pF"
```

```
paste("Cse = ", formatC((C2 * (1/(Qp^2) + 1)) * 10^12, digits = 1, format = "f"), "-pF", sep="")
```

```
## [1] "Cse = 25.2-pF"
```

```
paste("Rse = ", formatC(RL/((Qp^2) + 1), digits = 1, format = "f"), "-Ohms", sep="")
```

```
## [1] "Rse = 4.0-Ohms"
```

```
paste("XC = ", formatC(XC, digits = 1, format = "f"), "-Ohms", sep="")
```

```
## [1] "XC = 199.9-Ohms"
```

```
paste("C = ", formatC((1/(w*XC)) * 10^12, digits = 1, format = "f"), "-pF", sep="")
```

```
## [1] "C = 8.0-pF"
```

```
paste("C1 = ", formatC((-Cse * C / (C - Cse)) * 10^12, digits = 1, format = "f"), "-pF", sep="")
```

```
## [1] "C1 = 11.6-pF"
```

```
paste(formatC(L * 10^6, digits = 2, format = "f"), "-uH", sep="")
```

```
## [1] "0.32-uH"
```

```
## [1] " * C:/Users/merch/OneDrive/Documents/LTSpice/RF/impedanceTransformers/imp_transfx/bw_control.asc"
## [2] "L C 0 3.18055289143294e-07 Ipk=120 Rser=0.0 Cpar=0"
## [3] "Vcc N01 0 SINE(0 97103Meg) AC 1 Rser=0"
## [4] "Rt N01 C 10000"
## [5] "C1 C out 1.163297116301e-11"
## [6] "RL out 0 1000"
## [7] "C2 out 0 2.51192689211422e-11"
## [8] ";op"
## [9] ".ac lin 500 97Meg 103Meg"
## [10] ".backanno"
## [11] ".end"
## [12] ""
## [13] ""
## [14] ""
## [15] ""
```

Impedance Response for 2-MHz Bandwidth Circuit |
---|

## The response of the transformer has a peak at 100-MHz where it matches the source resistance of 10-k\(\Omega\) for the power amplifier. |