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그림 1.1에 전압 직렬 귀환 회로에 대하여 개념적인 형태로 표시하였다.

Could anyone explain why 표시하였다 not 표시핬어요 or 표시핬습니다 here? I am sure that there is some grammar I am missing now. Hope you could point it out so I can study it. Thanks.

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Both of 표시핬어요 or 표시핬습니다 are syntactically wrong. You would like to say 표시했어요 or 표시했습니다.

TL;DR

All of these forms actually mean same thing with different moods and tones.

  • 표시하였다.
  • 표시했어요.
  • 표시했습니다.

And the example sentence is speaking in very dry tone like a technical manual, and well matching form is first one. Though there're some syntactic rules, this is more idiomatic rather than syntactic.

Syntactic Explanation

In this case, 표시 delivers core meanings of display/show, and following -하였다, -했어요 and -했습니다 delivers verb, tense and mood/tones.

These tails can be decomposed into these parts.

하 였 다. (decompression of 했다)
하 였 어요. (decompression of 했어요)
하 였 습니다. (decompression of 했습니다)

is verb do, is tense did, and rest delivers tone like in this table.

  • -다. (dry tone)
  • -어요. (friendly tone)
  • -습니다. (formal tone)

Here's how -하였- gets compressed.

ㅎ ㅏ (ㅇ) ㅕ ㅆ     // `ㅇ` as initial consonant is just a placeholder of no sound. 
ㅎ (ㅏ + ㅕ) ㅆ     // compress two vowels into one.
ㅎ ㅐ ㅆ

Some parts can be decomposed further, but I don't know well about them.

Variations

In this sentence, a few parts are delivering dry-tone.

그림 1.1에 전압 직렬 귀환 회로에 대하여 개념적인 형태로 표시하였다.

If you intend friendly-tone, you can try this. Just compress -하여 to -해, and change ending form. Because decompressed form doesn't match well with friendly-tone.

그림 1.1에 전압 직렬 귀환 회로에 대해 개념적인 형태로 표시했어요.

Some people prefer a bit different form. This is more conversational feeling.

그림 1.1에 전압 직렬 귀환 회로에 대해서 개념적인 형태로 표시했어요.

Or in formal-tone.

그림 1.1에 전압 직렬 귀환 회로에 대해 개념적인 형태로 표시했습니다.

You can use decompressed form in formal-tone because it also matches.

그림 1.1에 전압 직렬 귀환 회로에 대하여 개념적인 형태로 표시했습니다.

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