How do I match the output of a transistor amplifier to 50 Ω?

I'm working on a simple single BJT transistor amplifier to amplify the output from an oscillator for use as a CW transmitter at 7 MHz.

I'm using an emitter follower to provide the power gain, and I'm trying to figure out how to match this to a 50 Ω antenna. I want to use an l-match but I don't know what the impedance at the output of the transistor is, so I don't know how to pick the component values.

I was thinking to just hook it up to a 50 Ω dummy load and iteratively pick values for the l-match trying to maximize the voltage across the 50 Ω load, but I don't think I'm going to be able to manually find optimal values for L and C. What is the correct way to go about doing this?

Here is the schematic:

• Can you provide a schematic of the intended emitter follower? It simplifys answering details.
– Jens
Commented Jul 18, 2022 at 3:45
• I added the schematic. Commented Jul 18, 2022 at 4:06
• This might be helpful: electronics.stackexchange.com/questions/169675/… Commented Jul 18, 2022 at 4:28
• I believe that in the broadcast context the impedance of the antenna might not be 50 (datasheet may have it), and they want you to add some inductors and capacitors before the antenna to make (antenna + components) equal 50. However, this only helps if your wires have a characteristic impedance of 50 - ordinary jumper wires don't. If the impedance of the antenna is already 50, and the wire is 50, then as far as antenna branch is concerned, you're good. No transmission line reflections from that branch. Commented Jul 18, 2022 at 9:32
• How much RF power are you designing for? The ~10mA DC emitter current only supports RF input up to about half-volt peak. Above that, you have (disastrous) 2nd-harmonic distortion, as current bottoms-out. So don't expect clean output above 2.5 mW. Commented Jul 18, 2022 at 12:01

Suppose you have this circuit:

simulate this circuit – Schematic created using CircuitLab

The AC impedance of the base of the BJT is equal to :

$$\ \frac{V_{T}}{I_{E}} = \beta r_{e}$$

where $$I_{E}$$ is equal to the DC emitter current(ignore AC sources)

The input impedance of the emitter follower is simply $$\beta (r_{e}+R_{E}) \left | \right |R_{b}$$

The output impedance of the emitter follower is $$r_{e}\left | \right |R_{E}\left | \right |Z_{L}$$

In your case the input of the BJT is fed from the voltage divider of R1||R2:

simulate this circuit

So the only thing that changes is the input resistance which will be equal to $$R_{b1}\left | \right |R_{b2} \left | \right |\beta (r_{e}+R_{E})$$

In order maximum transfer of power to the antenna which is your load $$Z_{L} = r_{e} \left | \right |R_{E}$$ and from that point on all the tools needed to solve this problem have been given to you by me.

• @TonyStewartEE75 The AC small signal analysis of the BJT gives Zin and Zout I think I have done it correctly... Commented Jul 18, 2022 at 4:35
• Reconsider that Rout is driven by a current buffer of a voltage source that is AC coupled . So Rout must be the voltage source impedance (0) divided by 𝛽. So you match it by adding 50 in series. However Re must also draw enough DC current to drive the peak AC current so it is also 50 ohms. Commented Jul 18, 2022 at 4:43
• No it is incorrect. Do you understand it is not a current source like the collector? But a current amplified voltage input source for AC being 0 ohms with some loss due to re Commented Jul 18, 2022 at 4:45
• "Do you understand it is not a current source like the collector?".What do you mean exactly? Commented Jul 18, 2022 at 4:56
• Do you know how to verify impedance by testing with a series R to get 50 % loss? Try that on your favorite simulator. Yet ee_student is correct on the goal to match the antenna to the delay line impedance and it ok to use a lower impedance emitter as long as it is stable. Commented Jul 18, 2022 at 12:47